How many ways can a school organization officers consisting of a president, a vice-president, a secretary, and a treasurer be formed from 6 males and 7 females, if;
a. Any of them is qualified to any position.
Choose the president as any of the 13 people.
Choose the vice-president as any of the 12 remaining people.
Choose the secretary as any of the 11 remaining people.
Choose the treasurer as any of the 10 remaining people.
13×12×11×10 = 13P4 = 17160
b. The president must be a male.
Choose the president as any of the 6 males.
Choose the vice-president as any of the 12 remaining people.
Choose the secretary as any of the 11 remaining people.
Choose the treasurer as any of the 10 remaining people.
6×12×11×10 = 6×12P3 = 7920
c. The president and the vice president must be a male and female respectively?
Choose the president as any of the 6 males.
Choose the vice-president as any of the 7 females.
Choose the secretary as any of the 11 remaining people.
Choose the treasurer as any of the 10 remaining people.
6×7×11×10 = 6×7×11P2 = 4620
d. The president must be a female but three particular females do not want to be included in the set of officers.
That's 6 males and only 4 females, since 3 females aren't considered.
That's 10 people to choose from.
Choose the president as any of the 4 females.
Choose the vice-president as any of the 9 remaining people.
Choose the secretary as any of the 8 remaining people.
Choose the treasurer as any of the 7 remaining people.
4×9×8×7 = 4×9P3 = 2016
Edwin
