Question

In: Statistics and Probability

COLLAPSE The student governing board at Milton University consists of 7 members: Andy, Bill, Cathy, David,...

COLLAPSE 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

Please explain your answers and show all the work.

Expert Solution

Men - Bill, David, Frank, Andy
Women - Cathy, Evelyn, Gina

A president and a secretary if one person can hold both offices

= 7 *7 = 49

there are 7 person for each job

· A president and a secretary if the president must be a female

CE, CG, CB, CD, CF, CA, EG, EB, ED, EF, EA, GB, GD, GF, GA.(15)

· A president and a secretary if the two officers must not be the same sex

= 4 * 3 + 3*4 = 24

note that there are 4 ways to select person for 1 post and 3 for other

and there are two ways to select if president will be selected from male or female , other will be fixed automatically

A president, a secretary, and a treasurer = 210

· A president, a secretary, and a treasurer, if the president must be a man and the other two must be women =24

· A president, a secretary, and a treasurer, if the secretary must be a woman and the other two must be men = 36

explanation :-

orchestra answered 2 years ago

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