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Answer :
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:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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
[tex]C_{10,3}*C_{5,2} = \frac{10!}{3!7!}*\frac{5!}{2!3!} = 1200[/tex]
His mother can get 3 arcade and 2 sports games is 1200 ways.
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Final answer:
The boy's mother can choose 3 arcade games and 2 sports games from his collection in 1200 different ways.
Explanation:
To solve this problem, we can use the concept of combinations. Since there are 10 arcade games and we need to choose 3, there are C(10, 3) ways to choose 3 arcade games. Similarly, there are C(5, 2) ways to choose 2 sports games from the 5 available. To find the total number of ways, we multiply these two combinations: C(10, 3) * C(5, 2).
Using the formula for combinations, C(n, r) = n! / (r!(n - r)!), we can calculate both combinations:
- C(10, 3) = 10! / (3!(10 - 3)!) = 120
- C(5, 2) = 5! / (2!(5 - 2)!) = 10
Now, we multiply the two combinations together: 120 * 10 = 1200. So, there are 1200 ways that the boy's mother can choose 3 arcade games and 2 sports games from his collection.
Learn more about Permutations and Combinations here:
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