The student governing board at Milton University consists of 7 members: Andy, Bill, Cathy, David, Evelyn, Frank, Gina. List and count the different ways of electing each of the following: · A president and a secretary if one person can hold both offices · A president and a secretary if the president must be a female · A president and a secretary if the two officers must not be the same sex · A president, a secretary, and a treasurer · A president, a secretary, and a treasurer, if the president must be a man and the other two must be women · A president, a secretary, and a treasurer, if the secretary must be a woman and the other two must be men
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.
List and count the different ways of electing each of the following:
· A president and a secretary if one person can hold both offices
· A president and a secretary if the president must be a female
· A president and a secretary if the two officers must not be the same sex
· A president, a secretary, and a treasurer
· A president, a secretary, and a treasurer, if the president must be a man and the other two must be women
· A president, a secretary, and a treasurer, if the secretary must be a woman and the other two must be men
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