A play has two roles for men and four roles for women if five men and 12 women tryout for these parts,in how many different ways can the director choose people for the roles
The men positions can be filled in (5)(4) or 20 ways.
The women position can be filled in (12)(11)(10)(9) or 11880 ways
Which is exactly what Steve had in
P(5,2) * P(12,4) = 20(11880) = 237600 ways
So go with Steve's answer.
5P2 * 12P4 = ?
can someone help me with this problem:There was a country concert held at the park. For every 5 men there were 3 women that went to the concert. If 72 total people attended the concert, how many men and how many women each attended the concert? Because i searched it and it gives me the wrong anwser.
To solve this problem, we can use combinations.
First, let's consider the roles for men. There are two roles and five men trying out. The director needs to choose two men for the roles. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
where C(n, r) is the number of combinations, n is the total number of items to choose from, and r is the number of items to choose.
In this case, n = 5 (number of men trying out) and r = 2 (number of roles for men). So the calculation would be:
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2!3!) = (5 x 4 x 3!) / (2! x 3!) = (5 x 4) / (2 x 1) = 10
Therefore, the director can choose two men for the roles in 10 different ways.
Now let's consider the roles for women. There are four roles and twelve women trying out. The director needs to choose four women for the roles. Using the same combination formula:
C(n, r) = n! / (r!(n-r)!)
In this case, n = 12 (number of women trying out) and r = 4 (number of roles for women). So the calculation would be:
C(12, 4) = 12! / (4!(12-4)!) = 12! / (4!8!) = (12 x 11 x 10 x 9!) / (4! x 9!) = (12 x 11 x 10) / (4 x 3 x 2 x 1) = 12 x 11 x 10 / 24 = 220
Therefore, the director can choose four women for the roles in 220 different ways.
To find the total number of different ways the director can choose people for the roles, we multiply the number of ways to choose men by the number of ways to choose women:
Total number of ways = 10 x 220 = 2,200
Therefore, the director can choose people for the roles in 2,200 different ways.