there are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6 person committee. how many committees are possible containing at most 1 faculty member?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
there are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6 person committee. how many committees are possible containing at most 1 faculty member?
At most 1 means 0 or 1 faculty member
If there are 0 faculty members then we have to select 6 members from (4+3)=7 student and office stuff
We can do that in 7C6 ways
If there are 1 faculty member then we can select the faculty member in 5C1 ways
We can select other (6-1) =5 members, from (4+3)=7 student and office stuff
We can do that in 7C5 ways
So total number of ways for 1 faculty member is (5C1)(7C5)
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