Shouln't the answer be 8C4 * 2 + 8C5 ?
The question is asking for number of committees Not the number of ways to form the committees
Could you explain the reason for multiplying by 2?
That was my mistake!! We do not need to multiply by 2.
I overthought the problem. I thought that the question is asking for number
of committees Not the number of ways
to form the committees
So I thought when we select any 4 people out of 8 to form a commitee, we are basically creating 2 committees. 4 selected people and 4 remaining. So we need to multiply 8C4 by 2. But I now know that 8C4 will cover all the remaining people as well.
So no need to multiply by 2.