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Answer :
There are 1200 ways for the boy's mother to get 3 arcades and 2 sports games from his collection.
We can use the combination formula which is:
nCr = n! / (r! * (n-r)!)
where n is the total number of items, r is the number of items to choose, and ! denotes the factorial function.
In this case, we want to choose 3 arcade games and 2 sports games from a collection of 10 arcade games and 5 sports games. So, we have:
Number of ways to choose 3 arcade games from 10 arcade games = 10C3 = 120
Number of ways to choose 2 sports games from 5 sports games = 5C2 = 10
Therefore, the total number of ways to choose 3 arcade games and 2 sports games is:
120 * 10 = 1200
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