SOLUTION: Given a group of students: G=(Allen,Brenda,Chad,Dorothy,Eric) or G=(A,B,C,D,E)count the different ways of choosing the following officers or representatives for student congress. A

Question 867481: Given a group of students: G=(Allen,Brenda,Chad,Dorothy,Eric) or G=(A,B,C,D,E)count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office.
A president, a secretary, and a treasurer, if the president must be a woman and the other two must be men

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There are two women: Brenda and Dorothy (B, D)

There are three men: Allen, Chad, and Eric (A,C,E)

There are two ways to choose the president. This is because "the president must be a woman".

So we could start off with Brenda (B) to have B __ __

The blank spaces represent slots for the secretary and treasurer.

There are 3 men to fill the second slot, then 3-1=2 men to fill the next slot. So 3*2 = 6 permutations possible. These permutations are:

BAC
BCA
BAE
BEA
BCE
BEC

Note: order matters and BAC is different from BCA (since Allen is secretary and Chad is treasurer in BAC; but Chad is secretary and Allen is treasurer in BCA)

If we picked Dorothy for president, then we get

DAC
DCA
DAE
DEA
DCE
DEC

There are 6 ways in the first group (with Brenda as president) and there are 6 ways in the second group (with Dorothy as president).

So there are 6+6 = 12 possible ways to have a president, a secretary, and a treasurer, if the president must be a woman and the other two must be men (given the candidates Allen,Brenda,Chad,Dorothy,Eric).

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