how many ways can 3 outfielders and 4 infidlers be chosen from 5 outfeilders and 7 infeilders?

From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How many different committees are possible if 2 men refuse to server together and 2 women will only serve together if they are together.

I have 7 friends, 2 tickets to the concert of the century, and I can’t go!I could give the tickets to friend #1 and #2, or #1 and #3, etc. How many different options are there? I've decided to make them vie for the tickets using a single elimination knock-out ping pong tournament. How many matches will I need to have?

A public health inspector wishes to inspect four restaurants by the end of the week. She has a list consisting of 26 "high- risk" premises, 68 “medium-risk" premises, and 95 "low-risk" premises that require inspections. How many different ways could a selection of the four restaurants be chosen that includes two “high-risk" and two “medium-risk" premises?

How many different committees can be formed from 6 teachers and 46 students if In how many ways can the committee of 5 members be selected? the committee consists of 3 teachers and 2 students?

A retail store is placing 5 mannequins on display side by side. Two of the male mannequins are dressed identically and two of the female mannequins are dressed identically. How many possibilities are there for the arrangement?

There are 5 women and 8 men in a department.  How many ways can this committee be selected if there must be 2 men and 2 women on the committee?

How many committees of six can be formed from 18 Republicans and 20 Democrats if three members of each party must be on the​ committee?