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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 :

Poltergeist

Answer:

116,280 ways.

Step-by-step 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

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

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

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