# Permutations and Combinations Quiz Set 020

### Question 1

How many 6 digit numbers ending in 0 can be formed with a given set of 6 distinct digits none of which is 0? Repetition of digits is not allowed.

A

720.

B

730.

C

750.

D

740.

Soln.
Ans: a

The units place is blocked by zero. The tens place has 6 options, the hundreds place also has (6 - 1) options, and so on. This is expressed as 6 × 5 × 4 × 3 × 2 × 1, which evaluates to 720.

### Question 2

In how many ways can 5 prizes be given to 2 students if each of them is equally eligible?

A

25.

B

35.

C

55.

D

45.

Soln.
Ans: a

The first has 5 options, the second also has 5 options, and so on. This is expressed as 5 × 5, which evaluates to 25.

### Question 3

What is the value of 7C2?

A

21.

B

31.

C

11.

D

41.

Soln.
Ans: a

7C2 is \${7 !}/{(7 - 2) ! × 2 !}\$ = 21.

### Question 4

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 5

The letters of the word 'PICTURE' 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. 