# Permutations and Combinations Quiz Set 003

### Question 1

Out of given 5 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

A

12000.

B

12010.

C

11990.

D

12020.

Soln.
Ans: a

We can make the selection in 4C3 × 5C2 + 4C2 × 5C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (4C3 × 5C2 + 4C2 × 5C3) = 12000.

### Question 2

5 men are standing in front of 7 cabins. In how many ways can they enter the cabins?

A

2520.

B

2525.

C

2518.

D

2521.

Soln.
Ans: a

The first has 7 options, the second has (7 - 1), and so on. This is expressed as 7P5, which evaluates to 2520.

### Question 3

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 4

How many words can be formed with 7 distinct consonants and 3 distinct vowels such that vowels stay together at the end of each word?

A

30240.

B

30250.

C

30230.

D

30260.

Soln.
Ans: a

We have to basically create two parts - one containing 7 consonants and the other containing 3 vowels. The consonants can be arranged in 7 ! ways, and vowels in 3 ! ways. The total count will be 7 ! × 3 ! = 30240.

### Question 5

How many possible outcomes are there if a die with 6 faces is cast and then a coin with 2 sides is tossed?

A

12.

B

17.

C

10.

D

13.

Soln.
Ans: a

The die can fall in 6 different ways, and a coin in 2 ways. So the outcomes are 2 × 6 = 12. 