# Permutations and Combinations Quiz Set 018

### Question 1

From a group of 9 boys and 6 girls, in how many ways can 2 boys and 2 girls be selected?

A

540.

B

550.

C

530.

D

560.

Soln.
Ans: a

The required count is 6C2 × 9C2 = 540.

### Question 2

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 a different train?

A

20.

B

25.

C

18.

D

21.

Soln.
Ans: a

The upward journey is possible in 5 ways, and the downward in 4 ways. So the outcomes are 5 × 4 = 20.

### Question 3

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 4

Section A of an exam has 3 questions, B has 6 questions and C has 4 questions. In how many ways can a student attempt the paper if he has to select one question from each of these sections?

A

72.

B

77.

C

70.

D

73.

Soln.
Ans: a

Clearly, it is 3 × 6 × 4 = 72.

### Question 5

Out of given 4 consonants and 3 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

A

2160.

B

2170.

C

2150.

D

2180.

Soln.
Ans: a

We can make the selection in 3C3 × 4C2 + 3C2 × 4C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (3C3 × 4C2 + 3C2 × 4C3) = 2160.