A committee of 5 people is to be chosen from a group of 8 women and 10 men.
How many diffferent committees are possible?
How many are possible if the following restrictions are enforced;
The committee must feature both men and women?
The committee must feature 3 women and two men?
The committee must have more women than men?

Question

A committee of 5 people is to be chosen from a group of 8 women and 10 men.
How many diffferent committees are possible?
How many are possible if the following restrictions are enforced;
The committee must feature both men and women?
The committee must feature 3 women and two men?
The committee must have more women than men?

jango_in_dtown · Answer

1st part 18C5=8568, since 5 people are chosen from (8+10)=18 people
second part we have to select in such a way that both men and women are there
Now let us find the number of cases where there are only men and the number of cases where there are only women and subtract it from the 8568 ways.. This will give the number of ways in which both men and women are featured/
only men =10C5=252
only women=8C5=56
so The committee must feature both men and women in 8568-(252+56)=8260 ways

jango_in_dtown · Answer

@painistatheart

anonymous · Answer

Oh wow thank you so much, this really helps! I wasn't sure if it was permutations or combinations!