Question

A group of Mathematics faculty at the local college consists of 10 women and 8 men. Five people are to be selected to go to a conference. How many different ways can a group of five people be selected from this group of 187 I In how many ways can five women be chosen from the group of 10 women? What is the probability that all women will be chosen to attend the conference?

Answer 1

There are 252 different ways to select five women from a group of 10 women. The probability that all women will be chosen to attend the conference is 0.0294.

Step-by-step explanation:

The number of ways to select a group of five people from a group of 10 women and 8 men can be found using combinations. The formula for combinations is C(n, r) = n!/((n-r)! * r!), where n represents the total number of items and r represents the number of items to be selected.

In this case, the number of ways to select five women from a group of 10 women can be calculated using C(10, 5) = 10! / ((10-5)! * 5!). Plugging in the values, we get:

C(10, 5) = 10! / (5! * 5!) = (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1) = 252.

So there are 252 different ways to select five women from the group of 10 women.

To find the probability that all women are chosen to attend the conference, we divide the number of ways to select five women from a group of 10 women by the total number of ways to select a group of five people from the entire group.

The total number of ways to select a group of five people from a group of 10 women and 8 men is C(18, 5) = 18! / ((18-5)! * 5!). Plugging in the values, we get:

C(18, 5) = 18! / (13! * 5!) = (18 * 17 * 16 * 15 * 14) / (5 * 4 * 3 * 2 * 1) = 8568.

Finally, we calculate the probability:

Probability = number of favorable outcomes / total number of outcomes = 252 / 8568 = 0.0294 (rounded to four decimal places).