Answer:
3003 ways
Step-by-step explanation:
You can basically choose 6 games from 14 games in total. This is essential a combination problem. We want the number of ways to choose 6 things from 14 things. The general formula for combinations is:
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Which tells us the number of ways to choose "r" things from a total of "n" things.
The factorial notation is:
n! = n * (n-1) * (n-2) * ....
Example: 3! = 3 * 2 * 1
Now, we know from the problem,
n = 14
r = 6
So, substituting, we get:
[tex]nCr=\frac{n!}{r!(n-r)!}\\14C6=\frac{14!}{6!(14-6)!}\\=\frac{14!}{8!*6!}\\=\frac{14*13*12*11*10*9*8!}{6!*8!}\\=\frac{14*13*12*11*10*9}{6*5*4*3*2*1}\\=3003[/tex]
You can choose in 3003 ways
