A committee with 7 senators on is divided into how many sub committees containing three?

Question

A committee of seven senators are divided into sub committees containing three. How many sub committees are there?

Answer 1

The combinations formula is the numbers of choices n taken r at a time.  So n = 7 and r=3.

 

C = [n!/(n-r)!r!] = 7!/[(7-3)!3!] = 7!/[4!*3!] = 7*6*5*4*3*2*1/[(4*3*2*1) * 3*2*1] quickly cancel out 4*3*2*1 as it's on the top and the bottom and reduces to 1, then you have (7*6*5)/6 which equals 35 different committees since order doesn't matter (meaning a group of- alice, bob and cindy is the same as a group with cindy, bob and alice).  if order matters then you use permutations, P = n!/(n-r)!   which would be 210 in this case.