# Permutations and Combinations Quiz Set 002

### Question 1

Section A of an exam has 6 questions, B has 2 questions and C has 3 questions. In how many ways can a student attempt the paper if he has to select one question from each of these sections?

A

36.

B

41.

C

34.

D

37.

Soln.
Ans: a

Clearly, it is 6 × 2 × 3 = 36.

### Question 2

There are 7 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

42.

B

47.

C

40.

D

43.

Soln.
Ans: a

The upward journey is possible in 7 ways, and the downward in 6 ways. So the outcomes are 7 × 6 = 42.

### Question 3

In how many ways can 4 letter words be formed by using a given set of 7 consonants?

A

840.

B

845.

C

838.

D

841.

Soln.
Ans: a

The first place can get any of the 7 consonants, the second place can then get (7 - 1), and likewise. This is expressed as 7 × 6 × 5 × 4, which evaluates to 840.

### Question 4

From a group of 5 boys and 7 girls, in how many ways can 2 boys and 2 girls be selected?

A

210.

B

220.

C

200.

D

230.

Soln.
Ans: a

The required count is 7C2 × 5C2 = 210.

### Question 5

How many 5 digit numbers ending in 0 can be formed with a given set of 7 distinct digits none of which is 0? Repetition of digits is not allowed.

A

840.

B

850.

C

870.

D

860.

Soln.
Ans: a

The units place is blocked by zero. The tens place has 7 options, the hundreds place also has (7 - 1) options, and so on. This is expressed as 7 × 6 × 5 × 4 × 1, which evaluates to 840. 