Permutations & Combinations Mcqs - Set 2

1)   A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

a. 150
b. 200
c. 250
d. 300
Answer  Explanation 

ANSWER: 200

Explanation:
The number of ways to select two men and three women = ⁵C₂ * ⁶C₃

= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200


2)   The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?

a. 720
b. 144
c. 120
d. 36
Answer  Explanation 

ANSWER: 144

Explanation:
The word MEADOWS has 7 letters of which 3 are vowels.

-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.


3)   Using all the letters of the word “NOKIA”, how many words can be formed, which begin with N and end with A?

a. 3
b. 6
c. 24
d. 120
Answer  Explanation 

ANSWER: 6

Explanation:
There are five letters in the given word.

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! = 6.


4)   Using all the letters of the word “THURSDAY”, how many different words can be formed?

a. 8
b. 8!
c. 7!
d. 7
Answer  Explanation 

ANSWER: 8!

Explanation:
Total number of letters = 8

Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.


5)   How many three letter words are formed using the letters of the word TIME?

a. 12
b. 20
c. 16
d. 24
Answer  Explanation 

ANSWER: 24

Explanation:
The number of letters in the given word is four.

The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24.


6)   A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?

a. 21
b. 12
c. 9
d. 108
Answer  Explanation 

ANSWER: 108

Explanation:
The boy can select one trouser in nine ways.

The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.


7)   There are 30 people in a group. If all shake hands with one another , how many handshakes are possible?

a. 870
b. 435
c. 30!
d. 29! + 1
Answer  Explanation 

ANSWER: 435

Explanation:
No explanation is available for this question!


8)   In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?

a. 120
b. 720
c. 4320
d. 2160
Answer  Explanation 

ANSWER: 720

Explanation:
No explanation is available for this question!


9)   In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

a. 10080
b. 4989600
c. 120960
d. None of these
Answer  Explanation 

ANSWER: 120960

Explanation:
No explanation is available for this question!


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

a. 40
b. 400
c. 5040
d. 2520
Answer  Explanation 

ANSWER: 5040

Explanation:
No explanation is available for this question!