# Permutations and Combinations Quiz Set 005

### Question 1

From a group of 4 boys and 5 girls, in how many ways can 2 boys and 2 girls be selected?

A

60.

B

70.

C

50.

D

80.

Soln.
Ans: a

The required count is 5C2 × 4C2 = 60.

### Question 2

From a group of 11 men and 8 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

7700.

B

7710.

C

7690.

D

7720.

Soln.
Ans: a

The required count is 8C3 × 11C2 + 8C2 × 11C3 = 7700.

### Question 3

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.

### Question 4

How many 5 digit numbers ending in 0 can be formed with a given set of 5 distinct digits none of which is 0? Repetition of digits is not allowed.

A

120.

B

130.

C

150.

D

140.

Soln.
Ans: a

The units place is blocked by zero. The tens place has 5 options, the hundreds place also has (5 - 1) options, and so on. This is expressed as 5 × 4 × 3 × 2 × 1, which evaluates to 120.

### Question 5

There are 5 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

25.

B

30.

C

23.

D

26.

Soln.
Ans: a

The upward journey is possible in 5 ways, and the downward also in 5 ways. So the outcomes are 5 × 5 = 25. 