There are five boys A, B, C, D, E who are to form a team to accomplish a particular task. How many distinct teams can be formed that contains at least one of the boys such that A & B don’t want to be in same team and also C & D don’t want to be in same team?

A. 15

B. 16

C. 17

D. 18

There are exactly 3 ways for A & B {(i) both A & B not selected, (ii) A selected & B not selected, (iii) A not selected & B selected} to be selected in the team.

Same ways there are exactly 3 ways for C & D to be selected in the team.

And there are exactly 2 ways for E i.e. to be selected or not selected in the team.

So total cases becomes = 3*3*2 = 18. But it includes the case when none of them is included in the team which we need to subtract to get the final answer as 18 – 1 = 17.

B. 16

C. 17

B

B

B

15

17.

17