# Permutations and Combinations Quiz Set 002

### Question 1

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 2

How many four letter words, with all the letters different, can be formed out of the letters of the word 'BIRTHPLACE'?

A

5040.

B

5050.

C

5030.

D

5060.

Soln.
Ans: a

This word has 10 different letters. The number of possibilities is 10P4 = 5040.

### Question 3

What is the value of 7C2?

A

21.

B

31.

C

11.

D

41.

Soln.
Ans: a

7C2 is \${7 !}/{(7 - 2) ! × 2 !}\$ = 21.

### Question 4

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

A

4.

B

9.

C

2.

D

5.

Soln.
Ans: a

The die can fall in 2 different ways, and a coin in 2 ways. So the outcomes are 2 × 2 = 4.

### Question 5

In how many ways can a secretary and general secretary be chosen from a committee of 13 members?

A

156.

B

161.

C

154.

D

157.

Soln.
Ans: a

The secretary can be any of the 13 members, the general-secretary can then be any of the (13 - 1) members. So the answer is 13 × (13 - 1) = 156.