Find the number of ways of selecting the committee with a maximum of 2 women and having at the maximum one woman holding one of the two posts on the committee.
Answers
Answer:
We have a committee that will have 4 people and at most 2 can be women. There are 6 men and 8 women that can be on the committee. How many ways can we select the 4 people?
There are two ways we can do this - we can figure out the number of ways the committee can be formed with 0, 1, and 2 women and add them up. The other way to do it is to figure out how many different ways the committee can be formed in all cases, then subtract out the ways that involve 3 and 4 women. Let's do it both ways to show that the answer will be the same.
All of these calculations will be Combinations (we don't care about the order of the picks, just the members of the committee). The general formula for a combination is to look at P, the population (or available number of people who can sit on the committee) and k, the number selected), with the general formula being:
Answer:
Therefore, there are 60 different ways to select the committee in this scenario. Consequently, choice is the right response (c).
Explanation:
There will be a committee of four, with a maximum of two women on it. The committee can have 6 men and 8 women on it. We can accomplish this in one of two ways: either we count the ways the committee can be made up of 0, 1, and 2 women and add those numbers together. The alternative method is to count all possible methods to form the committee, then take away the options that require 3 and 4 women. We should prove that the outcome will be the same in both directions. Combinations will be used for all of these calculations (the order of the picks is irrelevant; only the committee members will be considered).
The general formula for a combination is to consider P, the population (or the total number of persons who are eligible to serve on the committee), and k, the number chosen.
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