Question

The Math Honor Society has 100 members. There are 60 juniors and 40 seniors. The bylaws state that the president has to be a senior and the vice president has to be a junior. The secretary and treasurer can come from any class. How many ways can the president, vice president, secretary, and treasurer be elected assuming all 100 members want the jobs?


A)
22,814,400


B)
23,284,800


C)
23,760,000


D)
94,109,400

Answer 1

I have the answer; I'm just have a question about something.

Answer 2

First off, the answer is A right?

Answer 3

There are 40 choices for president and 60 choices for vice-president.
Once they are chosen, there are 98 choices for treasurer, and 97 choices for secretary.
40 x 60 x 98 x 97 = 22,814,400

Answer 4

Thats what I thought but initially I was thinking of using factorials.

Answer 5

@mathstudent55

Answer 6

The factorial part is used when you need to choose some elements out of a larger set and the order does not matter. Here each person is assigned a position.

Answer 7

Thank you. I have one question, but it is another unrelated math problem. Could you help with that?

Answer 8

If the question were like this, you'd have to do the factorial part:
The honor society has 40 seniors and 60 juniors. The president must be a senior and the vp must be a junior. In addition there must be two more members added to the executive committee. These two extra members can be any students. How many ways can the executive committe be chosen in?

Answer 9

What is difference between the original problem and this problem?

Answer 10

In this case, you'd start the same way with 40 choices for pres and 60 choices for vp.
The difference is that the two other committee members have the same designation, so if you choose students number 25 and 26 or 26 and 25, it's the same choice.

Answer 11

So here you'd do (40 x 60 x 98 x 97)2!

Answer 12

Post your other question in a new post and I'll look for it to help you.