1. A graduate school has 8,000 students (5,000 PhD students and 3,000 masters students). This school's executive board has 4 student members: a President, a VP of Operations, a VP of finance, and a VP of administration. a) How many ways are there to choose the executive board from all the students at this graduate school? b) How many ways are there to choose the executive board so that there is at least one masters student and one PhD student? (for any of the 4 positions) c) How many ways are there to choose the executive board if the VP positions have to be PhD students (the president can be either a PhD or Masters student)?
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.
1. A graduate school has 8,000 students (5,000 PhD students and 3,000 masters students). This school's executive board has 4 student members: a President, a VP of Operations, a VP of finance, and a VP of administration.
a) How many ways are there to choose the executive board from all the students at this graduate school?
b) How many ways are there to choose the executive board so that there is at least one masters student and one PhD student? (for any of the 4 positions)
c) How many ways are there to choose the executive board if the VP positions have to be PhD students (the president can be either a PhD or Masters student)?
d) How many ways are there to choose the executive board so that there is at least one masters student VP?
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