Combination Questions and Answers updated daily – Aptitude

Combination Questions: Solved 77 Combination Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

Combination Questions

1. In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that no two books on Hindi may not be together? 




SHOW ANSWER
Correct Ans:1540
Explanation:
Given:
No two Hindi books are together.
Number of English books = 21
Number of Hindi books = 19
Hindi books can be placed in the gaps between the English books.
Since the total number of English books = 21, It can be placed in 22 gaps including the ends.
Hence the number of combinations is given by =
22C19
We know that nCr = n! / [(n - r)! * r!]
22C19= (22*21*20*19! )/(19! * 3! )
= (22*21*20)/6
= 1540 ways.
Workspace



2. A question has two parts, Part A and Part B, each containing 8 questions. If the students have to choose 6 from part A and 5 questions from Part B, in how many ways can he choose the questions?




SHOW ANSWER
Correct Ans:1568
Explanation:
Given : Total 8 questions in part A of which 6 questions are chosen
= ⁸C₆
Total 8 questions in part B of which 5 questions are chosen = ⁸C₅
So the total number of ways = ⁸C₆ * ⁸C₅
= (8! / ((8-6)! * 6! )) * (8! / ((8 - 5)! * 5! ))
= (8! / (2! * 6!)) * (8! / (3! * 5! ))
= ((8*7*6!) / (2*6! )) * ((8*7*6*5! ) / (3*2*5! ))
= 28*56
= 1568 ways.
Workspace



3. At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. In how many ways a voter can vote?




SHOW ANSWER
Correct Ans:25
Explanation:
A voter can give either 1 vote, 2 votes or 3 votes.
Number of ways to give only 1 vote = 5C1 = 5
Number of ways to give only 2 vote = 5C2 = 10
Number of ways to give all 3 vote = 5C3 = 10
so, a voter can cast his vote by total : 5+10+10 = 25 ways.
Workspace



4. In how many different ways can the letters of the word ‘VIRTUAL’ be arranged such that all the vowels come together?




SHOW ANSWER
Correct Ans:720
Explanation:
The vowels in the word 'VIRTUAL' are I, U, A.
Number of ways to arrange the letters of the word'VIRTUAL'such that vowels always come together
= 5! x 3!
= (5 x 4 x 3 x 2 x 1) x (3 x 2 x 1)
= 120 x 6
= 720.
Workspace



5. In how many ways the five boys can be seated among six girls in such a way that no two boys sit together? 




SHOW ANSWER
Correct Ans:2520
Explanation:
Possible arrangement of boys and girls
B G B G B G B G B G B G B
where, B -- Boy
G --- Girl

Required number of ways, 7P5= 7!/2!
= (7 x 6 x 5 x 4 x 3 x 2)/2
= 2520
Workspace



6. In a language, there are six different words. A sentence can be formed by at least 2 words. If order of words is changed in a sentence, we get a different sentence. How many different sentences can be formed in this language? 




SHOW ANSWER
Correct Ans:1950
Explanation:
Here, different order gives different sentence.
Different sentences that can be formed = 6P₂ + 6P₃ + 6P₄ + 6P₅ + 6P₆
= [6!/(6-2)!] + [6!/(6-3)!] + [6!/(6-4)!] + [6!/(6-5)!] +[6!/(6-6)!]
= [6!/4!] + [6!/3!] + [6!/2!] + [6!/1!] +6!
= 30 + 120 + 360 + 720 + 720
= 1950
Workspace



7. A team of 7 children is to be selected out of 7 girls and 5 boys such that it contains at least 5 girls. In how many different ways can the selection be made? 




SHOW ANSWER
Correct Ans:246
Explanation:
The team of 7 children can be selected with atleast 5 girls are
When 5 girls and 2 boys are selected = 7C5 x 5C2
= [(7 x 6 x 5 x 4 x 3)/(1 x 2 x 3 x 4 x 5)] x [(5 x 4)/(1/2)]
= 21 x 10= 210

When 6 girls and 1 boys are selected = 7C6 x 5C1
= [(7 x 6 x 5 x 4 x 3 x 2)/(1 x 2 x 3 x 4 x 5 x 6)] x [5/1]
= 7 x 5 = 35

When 7 girls and no boy are selected = 7C7= 1

Required number of selection = (7C5 x 5C2) + (7C6 x 5C1) + 7C7
= 210 + 35 + 1
= 246
Therefore, total number of ways = 246.
Workspace



8. Five students are to be arranged on five chairs for a photograph. Three of these are girls and the rest are boys. Find out the number of ways in which all three girls do not occupy consecutive seats. 




SHOW ANSWER
Correct Ans:84
Explanation:

5 students can be arranged among themselves = 5Pâ‚… ways
= 5*4*3*2*1
=120 ways.

Assume that the 3 girls are one entity.
And the total number of ways they arranged among themselves = 3!
= 3*2*1 = 6 ways
Also, set of three girls and other students are arranged among themselves = 3!
= 3*2*1 = 6 ways
So,the total number of ways in which three girls are together = 6 * 6 = 36

Thus, number of ways in which all 3 girls will not occupy consecutive seats
= 120 – 36 = 84

Workspace



9. How many four digits number can be formed by using the digits 0, 2, 4, 6, 7 if repetition of digits is allowed?




SHOW ANSWER
Correct Ans:500
Explanation:
Total digits = 5
First place can be filled up by using only one of 4 digits (except 0, since 0 at the first place is meaningless).
Second place can be filled up by using all the five digits (as repetition is allowed).
Similarly, third and fourth place can be filled up by using all the five digits.
Thus,
Places: 0 0 0 0
Digit: 4 5 5 5
Total numbers = 4 × 5 × 5 × 5 = 500
Workspace



10. There are 5 blue flags, 4 red flags and 3 green flags, in Debu"™s wardrobe. He has to select 4 flags from this set. In how many ways can he select these four flags such that there is at least one blue flag and exactly one green flag in them (Do not consider that the flags are in pairs)?




SHOW ANSWER
Correct Ans:240
Explanation:
No of selection can be in following ways = (3C₁*5C₁*4C₂) + (3C₁*5C₂*4C₁) + (3C₁* 5C₃)
= [3*5*((4*3)/(1*2))] + [3*((5*4)/(1*2))*4] + [3*((5*4*3)/(1*2*3))]
= (3*5*6) + (3*10*4) + (3*10)
= 90 + 120 + 30
= 240
Workspace



11. How many 3 - letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?




SHOW ANSWER
Correct Ans:720
Explanation:
The word 'LOGARITHMS'' has 10 different alphabets
Hence, the number of 3-letter words (with or without meaning) formed by using these letters = 10P3
= 10*9*8
=720
Workspace



12. How many Permutations of the letters of the word APPLE are there? 




SHOW ANSWER
Correct Ans:60
Explanation:
In the given word “APPLE”, letter "P" is written twice.
So word APPLE contains 1A, 2P, 1L and 1E.
Required Permutations = 5! / 2!
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= 60
Workspace



13. Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? 




SHOW ANSWER
Correct Ans:6
Explanation:
There are five letters in the given word “NOKIA”
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 3 X 2 X 1 = 6
Workspace



14. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?




SHOW ANSWER
Correct Ans:209
Explanation:
Chances for selecting 4 children From 6 Boys (with atleast 1 boy) From 4 Girls
Chance 1 1 3 -> 6C1 X 4C3
= 6 X 4
= 24
Chance 2 2 2 -> 6C2 X 4C2
= 15 X 6
= 90
Chance 3 3 1 -> 6C3 X 4C1
= 20 X 4
= 80
Chance 4 4 0 -> 6C4
= 15
















Different ways to select 4 children (with atleast 1 boy) = 24 + 90 + 80 + 15 = 209
Workspace



15. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? 




SHOW ANSWER
Correct Ans:720
Explanation:
The vowels in the word 'LEADING' are E, A, I
Number of ways to arrange the letters of the word 'LEADING' such that vowels always come together = LDNG(EAI)
= 5! X 3!
= (5 x 4 x 3 x 2 x 1) X (3 x 2 x 1)
= 120 X 6
= 720
Workspace



16. In how many ways 6 people can be arranged in row, if one particular person always wants to stand in the rightmost corner? 




SHOW ANSWER
Correct Ans:5!
Explanation:
Out of 6 person one wants to be in the right most corner, so ignore him
Out of the remaining 5 people, they can be arranged in 5! ways.
Workspace



17. In how many ways a four digit even number can be formed by using the digits 4,5,9,8 exactly once. 




SHOW ANSWER
Correct Ans:12
Explanation:
Given
Four digit even number can be formed by using the digits 4,5,9,8
Since the number has to be a even digit number,the units digit has to be 4 or 8. First three places can be filled by remaining three digits.
Hence it is totally 6 x 2 = 12 ways
Answer is 12
Workspace



18. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? 




SHOW ANSWER
Correct Ans:63
Explanation:
Given
Total Men = 7
Total Women = 3
From total, agroup of 5 men and 2 women be made out
Required number of ways
=>(7C5 x 3C2)
=>( 7 * 6 * 5 * 4 * 3 * 2 * 1 ) / (5 * 4 * 3 * 2 * 1) x ( 3 * 2) / ( 2 * 1 )
=>( 7 * 3 ) x ( 3 )
=> 21 * 3
=> 63.
Workspace



19. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? 




SHOW ANSWER
Correct Ans:64
Explanation:
We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
= ( 3 x 6 x 5 / 2 x 1 ) + ( 3 x 2 / 2 x 1 x 6) + 1
= (45 + 18 + 1)
= 64
Workspace



20. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? 




SHOW ANSWER
Correct Ans:25200
Explanation:
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= (7C3 x 4C2)
= ( 7 x 6 x 5 / 3 x 2 x 1) x (4 x 3 / 2 x 1 )
= 210
Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120.

Therefore, Required number of ways = (210 x 120) = 25200
Workspace



Are you seeking for good platform for practicing Combination questions in online. This is the right place. The time you spent in Fresherslive will be the most beneficial one for you.

Online Test on Combination @ Fresherslive

This page provides important questions on Combination along with correct answers and clear explanation, which will be very useful for various Interviews, Competitive examinations and Entrance tests. Here, Most of the Combination questions are framed with Latest concepts, so that you may get updated through these Combination Online tests. Combination Online Test questions are granted from basic level to complex level.

Why To Practice Combination Test questions Online @ Fresherslive?

Combination questions are delivered with accurate answer. For solving each and every question, very lucid explanations are provided with diagrams wherever necessary.
Practice in advance of similar questions on Combination may improve your performance in the real Exams and Interview.
Time Management for answering the Combination questions quickly is foremost important for success in Competitive Exams and Placement Interviews.
Through Fresherslive Combination questions and answers, you can acquire all the essential idea to solve any difficult questions on Combination in short time and also in short cut method.
Winners are those who can use the simplest method for solving a question. So that they have enough time for solving all the questions in examination, correctly without any tense. Fresherslive provides most simplest methods to answer any tough questions. Practise through Fresherslive test series to ensure success in all competitive exams, entrance exams and placement tests.

Why Fresherslive For Combination Online Test Preparation?

Most of the job seekers finding it hard to clear Combination test or get stuck on any particular question, our Combination test sections will help you to success in Exams as well as Interviews. To acquire clear understanding of Combination, exercise these advanced Combination questions with answers.
You're Welcome to use the Fresherslive Online Test at any time you want. Start your beginning, of anything you want by using our sample Combination Online Test and create yourself a successful one. Fresherslive provides you a new opportunity to improve yourself. Take it and make use of it to the fullest. GOODLUCK for Your Bright Future.


Online Test for Data Interpretation
Online Test for C Language
FreshersLive - No.1 Job site in India. Here you can find latest 2022 government as well as private job recruitment notifications for different posts vacancies in India. Get top company jobs for both fresher and experienced. Job Seekers can get useful interview tips, resume services & interview Question and answer. Practice online test free which is helpful for interview preparation. Register with us to get latest employment news/rojgar samachar notifications. Also get latest free govt and other sarkari naukri job alerts daily through E-mail...
DMCA.com Protection Status