4) Suppose that a club with exactly 10members, whom we’ll call A, B, C, D, etc.,

Question

4)     Suppose that a club with exactly 10members, whom we’ll call A, B, C, D, etc., will choose apresident, a treasurer, and a secretary. (No one will hold morethan one office.)

(a)   If everyone is eligible, how many slates ofofficers are possible? (One slate would be D for president, C fortreasurer, H for secretary.)

(b)   If person E must be on the slate, how manyslates of officers are possible?

Question Details:

4)     Suppose that a club with exactly 10members, whom we’ll call A, B, C, D, etc., will choose apresident, a treasurer, and a secretary. (No one will hold morethan one office.)

(a)   If everyone is eligible, how many slates ofofficers are possible? (One slate would be D for president, C fortreasurer, H for secretary.)

(b)   If person E must be on the slate, how manyslates of officers are possible?

Explanation / Answer

1)To pick the president, there are 10 choices. Then when wepick the treasurer, there are 9 remaning choices of members. Andfinally when picking the secretary, we have 8 remaining choices.Thus, there are 10x9x8 = 720 slates possible. 2)If person E is selected as a president, then we will have 9remaining choices for a treasurer, and then 8 remaining choices fora secretary. Thus, there are 9x8 = 72 slates if E ispresident. If person E is selected as treasurer, there are also 9x8 = 72possible slates (same idea as previous) If person E is selected as secretary, there are also 9x8 = 72possible slates (same idea as previous) Thus, in total, there are 72+72+72 = 216 possible slates ifperson E must be on the slate If person E is selected as secretary, there are also 9x8 = 72possible slates (same idea as previous) Thus, in total, there are 72+72+72 = 216 possible slates ifperson E must be on the slate

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