# Permutations and Combinations Quiz Set 001

### Question 1

The letters of the word 'BEAUTY' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?

A

36.

B

46.

C

26.

D

56.

Soln.
Ans: a

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.

### Question 2

What is the value of 5C3?

A

10.

B

20.

C

0.

D

30.

Soln.
Ans: a

5C3 is \${5 !}/{(5 - 3) ! × 3 !}\$ = 10.

### 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 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 4

How many words can be formed with 6 distinct consonants and 2 distinct vowels such that vowels stay together at the end of each word?

A

1440.

B

1450.

C

1430.

D

1460.

Soln.
Ans: a

We have to basically create two parts - one containing 6 consonants and the other containing 2 vowels. The consonants can be arranged in 6 ! ways, and vowels in 2 ! ways. The total count will be 6 ! × 2 ! = 1440.

### Question 5

There are 6 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

30.

B

35.

C

28.

D

31.

Soln.
Ans: a

The upward journey is possible in 6 ways, and the downward in 5 ways. So the outcomes are 6 × 5 = 30.