How many committees of 4 can be made from a group of 20 republicans and 15 democrats if at least 1 republican and at least 1 democrat must be 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.
How many committees of 4 can be made from a group of 20 republicans and 15 democrats if at least 1 republican and at least 1 democrat must be on the committee?
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