A young boy sends his brother to pick 5 game-boy cartridges from his collection of 10 arcade and 5 sports games

Math Sep 29, 2020

A young boy sends his brother to pick 5 game-boy cartridges from his collection of 10 arcade and 5 sports games. How many ways are there that his brother will select 2 sports and 3 arcade games respectively?

Expert Solution

We have 15 games (10 arcade and 5 sports )totally, we need to find the number ways to select 2 sports and 3 arcade games.

Number of ways to select 2 sports and 3 arcade= 5C2*10C3

We know that nCr= n!/r!(n-r)!

=> [(5!)/2!(5-2)!]*[10!/3!(10-3)!]

=> [(4*5)/2]*[(8*9*10)/(1*2*3)]

=>[10]*[120]

=>1200
His brother can select the game in 1200 ways.

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