Permutation & Combinations – Aptitude Questions with Answers
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Answer: Option D Explanation: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).


2. 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? 

Answer: Option C Explanation: We may have(1 black and 2 nonblack) or (2 black and 1 nonblack) or (3 black).


3 . How many 4letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed? 

Answer: Option C Explanation: ‘LOGARITHMS’ contains 10 different letters.


4 . 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?  
Answer: Option D Explanation: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

5 . In a cricket championship, there are 21 matches. If each team plays one match with every other team, the number of teams is
 7
 9
 10
 None of these
Answer & Explanation
Let n be the number of teams.
^{n}C_{2} = 21
(n(n1)/2) = 21
⇒ n(n1) = 42 ∴
⇒ n = 7
6. In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is:
 32
 31
 30
 29
Answer & Explanation
The candidate will fail if he fails either in 1 or 2 or 3 or 4 or 5 subjects,
∴ Required number of ways ^{5}C_{1} + ^{5}C_{2} + ^{5}C_{3} + ^{5}C_{4} + ^{5}C_{5} = 31
7 . Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A) 25200  B) 52000 
C) 120  D) 24400 
Answer: A) 25200
Explanation:
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C37C3*4C24C2)
= 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! = 120
Required number of ways = (210 x 120) = 25200.
8 . There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?  
A. 10420  B. 11 
C. 11760  D. None of these 
Explanation:
We need to select 5 men from 8 men and 6 women from 10 women
Number of ways to do this
= ^{8}C_{5} × ^{10}C_{6}
= ^{8}C_{3} × ^{10}C_{4} [∵ ^{n}C_{r} = ^{n}C_{(nr)}]
=(8×7×63×2×1)(10×9×8×74×3×2×1)
=56×210=11760
9 . What is the value of 100 P 2 ?
a) 990 b) 9900 c) 9990 d ) None
Answer : Option B
Explanation :
100 P 2 = 100 * 99 = 9900
10 . What is the value of 58 C 3 ?
a) 30856 b)30868 c)30654 d) None of the above
Answer : Option A ) 30856
Explanation :
58 C3 = 58 * 57 * 56 / 3 * 2 * 1
= 30856