The dean of science wants to select a committee consisting of mathematicians and physicists to discuss a new curriculum. There are 15 mathematicians and 20 physicists at the faculty; how many possible committees of 8 members are there, if there must be more mathematicians than physicists (but at least one physicist) on the committee?
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.
A. Solve the following problems. Show your solutions
The dean of science wants to select a committee consisting of mathematicians and physicists to discuss a new curriculum. There are 15 mathematicians and 20 physicists at the faculty; how many possible committees of 8 members are there, if there must be more mathematicians than physicists (but at least one physicist) on the committee?
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