# Permutations and Combinations Quiz Set 013

### Question 1

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 2

How many possible outcomes are there if a die with 5 faces is cast and then a coin with 2 sides is tossed?

A

10.

B

15.

C

8.

D

11.

Soln.
Ans: a

The die can fall in 5 different ways, and a coin in 2 ways. So the outcomes are 2 × 5 = 10.

### Question 3

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.

### Question 4

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

A

2160.

B

2170.

C

2150.

D

2180.

Soln.
Ans: a

We can make the selection in 3C3 × 4C2 + 3C2 × 4C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (3C3 × 4C2 + 3C2 × 4C3) = 2160.

### Question 5

How many 6 digit numbers ending in 0 can be formed with a given set of 8 distinct digits none of which is 0? Repetition of digits is not allowed.

A

6720.

B

6730.

C

6750.

D

6740.

Soln.
Ans: a

The units place is blocked by zero. The tens place has 8 options, the hundreds place also has (8 - 1) options, and so on. This is expressed as 8 × 7 × 6 × 5 × 4 × 1, which evaluates to 6720.