# Permutations and Combinations Quiz Set 003

### Question 1

In how many ways can 4 prizes be given to 3 students if each of them is equally eligible?

A

64.

B

74.

C

94.

D

84.

Soln.
Ans: a

The first has 4 options, the second also has 4 options, and so on. This is expressed as 4 × 4 × 4, which evaluates to 64.

### Question 2

Out of given 7 consonants and 3 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 2 vowels and 3 consonants?

A

15120.

B

15130.

C

15110.

D

15140.

Soln.
Ans: a

We can make the selection in 3C3 × 7C2 + 3C2 × 7C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (3C3 × 7C2 + 3C2 × 7C3) = 15120.

### Question 3

How many 2 digit numbers can be formed with a given set of 6 distinct digits?

A

36.

B

46.

C

66.

D

56.

Soln.
Ans: a

The first place has 6 options, the second place also has 6 options, and so on. This is expressed as 6 × 6, which evaluates to 36.

### Question 4

What is the value of 5C3?

A

10.

B

20.

C

0.

D

30.

Soln.
Ans: a

5C3 is \${5 !}/{(5 - 3) ! × 3 !}\$ = 10.

### Question 5

There are 7 trains between two stations A and B. In how many ways can a student go from A to B and return by any of the available trains?

A

49.

B

54.

C

47.

D

50.

Soln.
Ans: a

The upward journey is possible in 7 ways, and the downward also in 7 ways. So the outcomes are 7 × 7 = 49.