Question

A group of 15 of your friends wants to go to a concert. Unfortunately, you only have 10 tickets available to give to your friends. How many different groups of friends could you take to the concert?

Answer 1

combinations of 15 ten at a time

n = 15
r = 10

C(n,r) = n!/[ r!(n-r)! ]

= 15! /[ 10! (5!) ]

= 15*14*13*12*11 /(5*4*3*2)

= 15/15 * 14/2 * 13 * 12/4 * 11

= 7 * 13 * 3 * 11

= 3003