Further Applications

Question

Your Friend has 16 different magazines and five different DVDs he is willing to loan to you. If you take three magazines and three DVDs, how many different collections could you end up with?

I need to use the ! Notation (or whatever that one is called)

Answer 1

Hi Kathrina!

 

This is a Combinations problem, because you are choosing a sub-group out of a larger group and order does not matter.

 

The Combinations formula is n! / [r! * (n - r)!]

n represents the total number of objects

r represents the sub-group of objects

! represents factorial, which is the number multiplied by every smaller integer until you reach 1.

 

MAGAZINES:

You are choosing 3 magazines out of 16 total magazines.  So, n = 16 and r = 3.

16! / [3! * (16 - 3)!] = 

16! / (3! * 13!)

 

DVDs:

You are choosing 3 DVDs out of 5 total DVDs.  So, n = 5 and r = 3.

5! / [3! * (5 - 3)!] =

5! / (3! * 2!)

 

COLLECTIONS:

To determine the number of different collections you could end up with, multiply the combinations of magazines by the combinations of DVDs.

[16! / (3! * 13!)] * [5! / (3! * 2!)] =

(16! * 5!) / (3! * 13! * 3! * 2!)