Question

The Tiny State College Student Advisory Board has rules to the effect that the officers of the board (i.e., Chairperson, Vice-Chairperson, and Treasurer) must always include at least one in-state student and at least one senior. The 150 Student Council consists of 6 members: 1 in-state senior, two in-state stude who are not seniors, 1 out-of-state senior, and two out-of-state students wn not seniors. In how many ways can the officers of the Student Advisory Bog selected from these 6 Student Council members if they must obey the rules that if individual members switch offices, this produces a different Board.

Answer 1

P (6, 3) – p (6, 4) – p (6, 2) = 270

Explanation:

The 150 student council consist of 6 members.

Included at least one in-state student and at least one senior.

There are total 6 members: in which,

1 in- state senior,

2 in state non-senior,

1 out of state senior and

2 out of state non-senior.

Total member are 6 and we selected 3. So p (6, 3)

The way team will have only non-senior = p (6, 4)

The way team will have out of state = p (6, 2)

Subtracting the total we get:

P (6, 3) – p (6, 4) – p (6, 2) = 6x5x4 – 6 x 5 x 4 x3 – 6x 5

= 30 x 4 – 30 x 12 – 30

= 120 – 360 – 30

=- 270