# Permutations and Combinations Quiz Set 018

### Question 1

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 2

From a group of 4 men and 6 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

180.

B

190.

C

170.

D

200.

Soln.
Ans: a

The required count is 6C3 × 4C2 + 6C2 × 4C3 = 180.

### Question 3

In how many ways can 4 different types of ice-creams be distributed among 3 boys?

A

24.

B

29.

C

22.

D

25.

Soln.
Ans: a

The first can get any of the 4 ice-creams, the second can then get (4 - 1), and so on. This is expressed as 4P3, which evaluates to 24.

### Question 4

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.

### Question 5

In how many ways can 7 different types of ice-creams be distributed among 5 boys?

A

2520.

B

2525.

C

2518.

D

2521.

Soln.
Ans: a

The first can get any of the 7 ice-creams, the second can then get (7 - 1), and so on. This is expressed as 7P5, which evaluates to 2520.