# Permutations and Combinations Quiz Set 001

### Question 1

Section A of an exam has 2 questions, B has 3 questions and C has 8 questions. In how many ways can a student attempt the paper if he has to select one question from each of these sections?

A

48.

B

53.

C

46.

D

49.

Soln.
Ans: a

Clearly, it is 2 × 3 × 8 = 48.

### Question 2

From a group of 6 boys and 7 girls, in how many ways can 2 boys and 2 girls be selected?

A

315.

B

325.

C

305.

D

335.

Soln.
Ans: a

The required count is 7C2 × 6C2 = 315.

### Question 3

In how many ways can 9 different types of ice-creams be distributed among 5 boys?

A

15120.

B

15125.

C

15118.

D

15121.

Soln.
Ans: a

The first can get any of the 9 ice-creams, the second can then get (9 - 1), and so on. This is expressed as 9P5, which evaluates to 15120.

### Question 4

Out of given 8 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 2 vowels and 3 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 5

How many 3 digit numbers can be formed with a given set of 6 distinct digits?

A

216.

B

226.

C

246.

D

236.

Soln.
Ans: a

The first place has 6 options, the second place also has 6 options, and so on. This is expressed as 6 × 6 × 6, which evaluates to 216.