there are 8 men and 9 women on a committee. in how many ways can a sub committee of 2 and 3 women be chosen?
What is
C(8,2) x C(9,3) ?
To find the number of ways to choose a subcommittee of 2 men and 3 women from a committee of 8 men and 9 women, we can use the concept of combinations.
First, let's calculate the number of ways to choose 2 men from a group of 8. This can be done using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.
So, for the men, we have C(8, 2) = 8! / (2!(8-2)!) = 8! / (2!6!) = (8 * 7) / (2 * 1) = 28.
Next, let's calculate the number of ways to choose 3 women from a group of 9. Using the same combination formula, we get C(9, 3) = 9! / (3!(9-3)!) = 9! / (3!6!) = (9 * 8 * 7) / (3 * 2 * 1) = 84.
Finally, we need to determine the number of ways to combine the selected men and women. Since they are independent choices, we multiply the two results together:
Number of ways = 28 * 84 = 2352.
Therefore, there are 2352 ways to choose a subcommittee of 2 men and 3 women from the given committee.