Assume that a committee consists of 12 people including the chairperson and that the chairperson must select a committee of 3 people from the other 11 members of the committee.
In how many ways can this be done?
So....I tried 11*10*9 because im not counting the chairperson (starting with 11)...and then there are three other positions. it is the wrong answer tho and im not sure what I'm doing wrong. pleaseeee help!
165
To determine the number of ways to select a committee of 3 people from the remaining 11 members, you are on the right track in considering the number of choices for each position.
However, the approach of multiplying 11 * 10 * 9 is incorrect because it accounts for the selection of all 3 positions independently, assuming each selected position is distinct.
Since the order in which the positions are filled does not matter, you need to consider the concept of combinations rather than permutations. In this case, you need to use the combination formula, which is denoted as "nCr".
The formula for combinations is: nCr = n! / (r!(n-r)!), where n is the total number of objects to choose from and r is the number of objects to be chosen.
In this case, you need to find the number of ways to select 3 people from a pool of 11 members, so n = 11 and r = 3.
Using the combination formula, the calculation becomes: 11C3 = 11! / (3!(11-3)!) = (11! / (3!8!)) = (11 * 10 * 9) / (3 * 2 * 1) = 165.
Thus, there are 165 different ways to select a committee of 3 people from the remaining 11 members.