If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it? Pick.
A) 8 B) 24 C) 32 D) 56 E) 192
let AABBCCDD is the group with same letter representing a sibling pair.   total # ways to select 3 from 8 is 8C3=56   Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it   committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,32 and D   = 4 * (2322*6321) = 24   Hence Answer = 56-24= 
<gadget id="calculator">56-24</gadget>
<output>32</output>
32   ANS:32
<result>C</result>
If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it?