A law firm has ten male and ten female lawyers.
A committee of five- two male lawyers and three female lawyers, is to be chosen to represent the firm at a conference. How many committees are possible?
How do I solve this?
wtf does that mean
To solve this problem, you can use the combination formula, which gives the number of ways to choose a group of items from a larger set, without regard to the order in which they are selected.
The formula for calculating combinations is:
C(n, r) = n! / (r!(n-r)!)
In this case, you want to choose 2 males from a group of 10, and 3 females from a group of 10. Since these choices need to be made simultaneously, you can multiply the two combinations together to get the total number of committees possible.
First, calculate the number of combinations for choosing 2 males from 10:
C(10, 2) = 10! / (2!(10-2)!) = 10! / (2!8!) = (10 * 9) / (2 * 1) = 45
Next, calculate the number of combinations for choosing 3 females from 10:
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Now, multiply the two results together to get the total number of committees possible:
45 * 120 = 5,400
Therefore, there are 5,400 possible committees that can be formed.
To solve this problem, we can use combinations, a mathematical concept that calculates the number of ways to select a group of items without regard to the order in which they were chosen.
First, let's consider the number of ways to choose two male lawyers from a pool of ten. This can be calculated using a combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to be chosen.
In this case, we have n = 10 male lawyers and we need to choose k = 2 of them. So the number of ways to choose two male lawyers is C(10, 2) = 10! / (2!(10-2)!) = (10*9) / (2*1) = 45.
Next, let's consider the number of ways to choose three female lawyers from a pool of ten. Using the same formula, we have n = 10 female lawyers and k = 3 to be chosen. So the number of ways to choose three female lawyers is C(10, 3) = 10! / (3!(10-3)!) = (10*9*8) / (3*2*1) = 120.
Now, we can calculate the total number of possible committees by multiplying the number of ways to choose two male lawyers by the number of ways to choose three female lawyers. So the total number of committees is 45 * 120 = 5400.
Therefore, there are 5400 possible committees that can be chosen to represent the law firm at the conference.
There are 10C3 ways to pick the females, and 10C2 ways to pick the males.
So, that makes 10C3 * 10C2 ways to form the committee.