Question

A young boy asks his mother to get 5 Game Boy cartridges from his collection of 10 arcade and 5 sports games. How many ways are there that his mother can get 3 arcade and 2 sports games?

Answer 1

Answer:

His mother can get 3 arcade and 2 sports games is 1200 ways.

Step-by-step explanation:

For a game, the order is not important.

For example, buying FIFA 20 and then Madden NFL 20 is the same outcome as buying Madden NFL 20 and then FIFA 20. So we use the combinations formula to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, we have that:

10 arcade games

5 sports games

How many ways are there that his mother can get 3 arcade and 2 sports games?

3 arcade from a set of 10 and 2 sports from a set of 5. So

$C_{10,3}*C_{5,2} = \frac{10!}{3!7!}*\frac{5!}{2!3!} = 1200$

His mother can get 3 arcade and 2 sports games is 1200 ways.