Question

A delegation of 4 people is to be selected from 5 women and 6 men. Find the number of possible delegation if (a) there are no restrictions, (b) there is at least 1 women, (c) there are at least 2 women
One of the men cannot get along with one of the women. Find the number of delegations which include this particular man or woman, but not both.

Answer 1

if there are no restrictions, you need to compute the number of ways to choose 4 out of ten
called "ten choose four" written as
\[\dbinom{10}{4}\] and computed as
\[\dbinom{10}{4}=\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\]
cancel first, multiply last

Answer 2

What about the last one 'One of the men cannot get along with one of the women. Find the number of delegations which include this particular man or woman, but not both.'?