Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, list and count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office.
-Three representatives, if two must be female and one must be male
A)BDA, BDC, BDE, BAD, BCD, BED;6
B)BDA, BDC, BDE, DBA, DBC; 5
C)BDA, BDC, BDE; 3
D)BDA, BDC; 2

Question

Quizplus · Accepted Answer

Given the condition that two representatives must be female and one must be male, and assuming B and D are females and A, C, E are males, the combinations where two females and one male are chosen would be BDA, BDC, and BDE. This accounts for all combinations where Brenda and Dorothy are chosen alongside one of the males (Allen, Chad, Eric).

Given a Group of Students: G = {Allen, Brenda, Chad