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
