Permutations and Combinations Quiz Set 008

Question 1

The letters of the word 'TUESDAY' have to be arranged such that the vowels come together. How many different ways are possible?

A

720.

B

730.

C

710.

D

740.

Soln.
Ans: a

This word has 7 letters, out of which 4 are consonants and 3 are vowels. The vowels have to occupy three contiguous positions. This triad can be arranged in 3! ways like this: we can place 3 vowels in first place, 2 in second place and 1 in the third place, giving 3 × 2 × 1 = 6 permutations. Next, we have to arrange the 4 consonants and the triad treated as one letter, giving 5! = 120 possibilities. So the total possibilities are 6 × 120 = 720.

Question 2

In how many ways can a secretary and general secretary be chosen from a committee of 19 members?

A

342.

B

347.

C

340.

D

343.

Soln.
Ans: a

The secretary can be any of the 19 members, the general-secretary can then be any of the (19 - 1) members. So the answer is 19 × (19 - 1) = 342.

Question 3

How many four letter words, with all the letters different, can be formed out of the letters of the word 'BLACKSMITH'?

A

5040.

B

5050.

C

5030.

D

5060.

Soln.
Ans: a

This word has 10 different letters. The number of possibilities is 10P4 = 5040.

Question 4

In how many ways can 9 different types of ice-creams be distributed among 5 boys?

A

15120.

B

15125.

C

15118.

D

15121.

Soln.
Ans: a

The first can get any of the 9 ice-creams, the second can then get (9 - 1), and so on. This is expressed as 9P5, which evaluates to 15120.

Question 5

The letters of the word 'MEXICO' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?

A

36.

B

46.

C

26.

D

56.

Soln.
Ans: a

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.