# Permutations and Combinations Quiz Set 004

### Question 1

There are 8 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

56.

B

61.

C

54.

D

57.

Soln.
Ans: a

The upward journey is possible in 8 ways, and the downward in 7 ways. So the outcomes are 8 × 7 = 56.

### Question 2

How many possible outcomes are there if a die with 3 faces is cast and then a coin with 2 sides is tossed?

A

6.

B

11.

C

4.

D

7.

Soln.
Ans: a

The die can fall in 3 different ways, and a coin in 2 ways. So the outcomes are 2 × 3 = 6.

### Question 3

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 4

There are 8 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

64.

B

69.

C

62.

D

65.

Soln.
Ans: a

The upward journey is possible in 8 ways, and the downward also in 8 ways. So the outcomes are 8 × 8 = 64.

### Question 5

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.