A committee of four is to be selected from a group of fourteen people. How many different committees are possible, given the following conditions? (a) There is no distinction between the responsibilities of the members. (b) One person is the chair, and the rest are general members. (c) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.
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 committee of four is to be selected from a group of fourteen people. How many different committees are possible, given the following conditions?
(b) One person is the chair, and the rest are general members.
(c) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.
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