# Permutations and Combinations Quiz Set 006

### 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 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.

### Question 3

6 men are standing in front of 8 cabins. In how many ways can they enter the cabins?

A

20160.

B

20165.

C

20158.

D

20161.

Soln.
Ans: a

The first has 8 options, the second has (8 - 1), and so on. This is expressed as 8P6, which evaluates to 20160.

### Question 4

From a group of 9 men and 5 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

1200.

B

1210.

C

1190.

D

1220.

Soln.
Ans: a

The required count is 5C3 × 9C2 + 5C2 × 9C3 = 1200.

### Question 5

How many 2 digit numbers can be formed with a given set of 6 distinct digits?

A

36.

B

46.

C

66.

D

56.

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, which evaluates to 36.