Question

A town library is considering loaning video games, and surveyed its membership to ask their 4 favorite PlayStation 3 Games from among the following six: Gran Turismo, Call of Duty 4, Metal Gear Solid 4, Little Big Planet, Grand Theft Auto 5, & Final Fantasy 13. How many different possible sets of four favorites are there?
According to the textbook, the answer should be 15, but I'm a bit lost. What are the steps I need to take or the formula I need to use in order to get this answer?

Answer 1

Answer:

• 15 sets

Step-by-step explanation:

You need to find the combinations of 4 out of possible 6.

Use formula:

• $_nC_r=n!/r!(n-r)!$

where

• $_nC_r$  = number of combinations
• n = total number of objects in the set
• r = number of choosing objects from the set
• n!     = 1*2*3*...*n (in case you don't know the factorials)

In our case n = 6, r = 4, substitute these into equation:

• $_6C_4=6!/4!2! = 5*6*4!/4!*2 = 30/2 =15$