A Police department with 12 male and 8 female officers must select 6 officers to attend a conference on improving community relations. How many different selections are possible given the following conditions?a) Any mixture of male and female officers is allowed.b) There must be 3 male and 3 female officers at the conference.
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 Police department with 12 male and 8 female officers must select 6 officers to attend a conference on improving community relations. How many different selections are possible given the following conditions?a) Any mixture of male and female officers is allowed.b) There must be 3 male and 3 female officers at the conference.
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