Question

Questions a-e are based on the scenario that a president, treasurer, and secretary, all different, are to be chosen from a club consisting of 10 people. Calculate the number of different choices of officers possible if a. there are no restrictions. b. A and B will not serve together. c. C and D will serve together or not at all. d. E must be an officer. e. F will serve only if he is president.

Answer 1

Answer AND Step-by-step explanation:

president, treasurer, and secretary

total: 10 people

people: A, B, C, D, E, F, G, H, I, J

Calculate the number of different choices of officers possible if:

a. there are no restrictions.

10.9.8 = 720

b. A and B will not serve together.

Total - combinations that they are together

1 (A president) . 1 (B treasure) . 8 = 8 OR

1 (A president) . 1 (B secretary) . 8 = 8 OR

1 (A treasure) . 1 (B president) . 8 = 8 OR

1 (A treasure) . 1 (B secretary) . 8 = 8 OR

1 (A secretary) . 1 (B president) . 8 = 8 OR

1 (A secretary) . 1 (B treasure) . 8 = 8 OR

8.6 = 48

720 - 48 = 672

c. C and D will serve together or not at all.

C and D serve together:

1 (C president) . 1 (D treasure) . 8 = 8 OR

1 (C president) . 1 (D secretary) . 8 = 8 OR

1 (C treasure) . 1 (D president) . 8 = 8 OR

1 (C treasure) . 1 (D secretary) . 8 = 8 OR

1 (C secretary) . 1 (D president) . 8 = 8 OR

1 (C secretary) . 1 (D treasure) . 8 = 8 OR

8.6 = 48

Not at all

8.7.6 = 336

Total = 48 + 336 = 384

d. E must be an officer.

E president:

1.9.8 = 72 OR

E secretary:

1.9.8 = 72 OR

E treasure:

1.9.8 = 72

72.3 = 216

e. F will serve only if he is president.

1.9.8 = 72