Question

As a television executive, you have been given 21 shows to choose from to run during your prime time slots each week. If you have to choose 7 shows to run on your network, how many ways can you choose which shows to pick up?

Answer 1

116,280 ways.

Explanation:

In choosing the shows, the order in which you pick them does not matter; therefore it is a combination. Thus, the number ways you can choose 7 shows from 21 is

`(21!)/(7!(21-7)!) = (21!)/(7!\:14!)=(21*20*19*18*17*16*15)/(7*6*5*4*3*2*1) \\\\= 116,280.`

You can choose 7 shows from 21 in 116,280 ways.