There are four distinct pairs of brothers and sisters. In how many ways can a committee of 3 be formed and NOT have siblings in it?

a)8

b)24

C)32

d)56

e) 80

why is my approach wrong ?

My approach :

4C3 + 4C3 + (4C2 * 3C1) + (4C2 * 3C1)

selecting all brothers + all sisters + 2 brothers and 1 sister of 3 + 2 sisters and 1 brother of 3.

solution : 32

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