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lacrotix

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Hi there. I have a question about combinations at the Math 12 Principles level.

From a group of 5 student representatives, 3 will be chosen to work on the dance committee. Also, each committee must have a chairperson. How many committees are possible?

So I solved this question with

5 nCr 3 x 3 nCr 1 = 30

In which the first part of the equation finds all the possible committees that can be made, and the second part of the equation lists how many different leaders can be chosen from the sub-committee of three I just made.However, I don't see why I can't use this:

5 nCr 2 x 5 nCr 1 = 50

Where the first part chooses a combination of two followers and the second part chooses a combination of one leader for the sub-committee of three people.

Any ideas?

## Homework Statement

From a group of 5 student representatives, 3 will be chosen to work on the dance committee. Also, each committee must have a chairperson. How many committees are possible?

## The Attempt at a Solution

So I solved this question with

5 nCr 3 x 3 nCr 1 = 30

In which the first part of the equation finds all the possible committees that can be made, and the second part of the equation lists how many different leaders can be chosen from the sub-committee of three I just made.However, I don't see why I can't use this:

5 nCr 2 x 5 nCr 1 = 50

Where the first part chooses a combination of two followers and the second part chooses a combination of one leader for the sub-committee of three people.

Any ideas?

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