## Quant Question Of The Day: 45

# Counting

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?

1. 15

2. 16

3. 17

4. 18

5. None of these

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A,B,C,D,E,AC,BC,CE,DE,AD,BD,ACE,AE,BE,ADE,CBE,DBE = 17

SORRY, THE CORRECT ANSWER IS A,B,C,D,E,AC,BC,CE,DE,AD,BD,ACE,AE,BE,ADE,CBE,DBE= 17

17

16

One boy each – 5

Pair of boys – 8

Group of 3 boys – 4

Total distinct teams = 17

17

Correct me if m wrong about my method

A-3 ways

B-3

C-3

D-3

E-5 ways

Sum of all 17

7

17

Why 1 is subtracted in the end?