# Permutations and Combinations Quiz Set 012

### Question 1

How many 3 digit numbers can be formed with a given set of 5 distinct digits?

A

125.

B

135.

C

155.

D

145.

Soln.
Ans: a

The first place has 5 options, the second place also has 5 options, and so on. This is expressed as 5 × 5 × 5, which evaluates to 125.

### Question 2

Out of given 8 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

A

53760.

B

53770.

C

53750.

D

53780.

Soln.
Ans: a

We can make the selection in 4C3 × 8C2 + 4C2 × 8C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (4C3 × 8C2 + 4C2 × 8C3) = 53760.

### Question 3

From a group of 7 men and 4 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

294.

B

304.

C

284.

D

314.

Soln.
Ans: a

The required count is 4C3 × 7C2 + 4C2 × 7C3 = 294.

### Question 4

What is the value of 6P3?

A

120.

B

130.

C

110.

D

140.

Soln.
Ans: a

6P3 is \${6 !}/{(6 - 3) !}\$ = 120.

### Question 5

Out of given 7 consonants and 3 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

A

15120.

B

15130.

C

15110.

D

15140.

Soln.
Ans: a

We can make the selection in 3C3 × 7C2 + 3C2 × 7C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (3C3 × 7C2 + 3C2 × 7C3) = 15120. 