# Permutations and Combinations Quiz Set 017

### Question 1

In how many ways can a secretary and general secretary be chosen from a committee of 17 members?

A

272.

B

277.

C

270.

D

273.

Soln.
Ans: a

The secretary can be any of the 17 members, the general-secretary can then be any of the (17 - 1) members. So the answer is 17 × (17 - 1) = 272.

### Question 2

How many possible outcomes are there if a die with 6 faces is cast and then a coin with 2 sides is tossed?

A

12.

B

17.

C

10.

D

13.

Soln.
Ans: a

The die can fall in 6 different ways, and a coin in 2 ways. So the outcomes are 2 × 6 = 12.

### Question 3

In how many ways can 4 different types of ice-creams be distributed among 3 boys?

A

24.

B

29.

C

22.

D

25.

Soln.
Ans: a

The first can get any of the 4 ice-creams, the second can then get (4 - 1), and so on. This is expressed as 4P3, which evaluates to 24.

### 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

Section A of an exam has 3 questions, B has 6 questions and C has 5 questions. In how many ways can a student attempt the paper if he has to select one question from each of these sections?

A

90.

B

95.

C

88.

D

91.

Soln.
Ans: a

Clearly, it is 3 × 6 × 5 = 90. 