I feel kind of stupid asking this but I am not seeing the "fast" way to solve this. I know how to solve this using a financial calculator with nCr function, but the explanation is not sufficient for me. Short of counting out all the possibilities, what is not clicking here for me? Am I supposed to do the factorial math?
A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?
To find the total number of possible committees, we need to determine the number of different five-person groups that can be formed from a pool of 8 candidates. We will use the anagram method to solve this combinations question. First, let's create an anagram grid and assign 8 letters in the first row, with each letter representing one of the candidates. In the second row, 5 of the candidates get assigned a Y to signify that they were chosen for a committee; the remaining 3 candidates get an N, to signify that they were not chosen:
A B C D E F G H
Y Y Y Y Y N N N
The total number of possible five-person committees that can be created from a group of 8 candidates will be equal to the number of possible anagrams that can be formed from the word YYYYYNNN = 8! / (5!3!) = 56. Therefore, there are a total of 56 possible committees.
