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1. The problem statement, all variables and given/known data

Six musical instruments are available for loan. Assuming all are loaned, in how many different ways can these be assigned to the four musicians in the graduate music ensemble such that each instrument is loaned to one musician, each musician gets at least one instrument and no musician has more than three instruments on loan? Give answer as a whole number.

2. Relevant equations

Combination equation

3. The attempt at a solution

At first, I tried to solve this problem based on other similar problem's solution.

Here's how I tried:

There are two possibilities:

a - a student having 3 instruments and others have only one.

b - two students having two instruments and the rest have only one.

event a:[C(4,1) x C(6,3) x C(3,1) x C(3,1) x C(3,1) divided by 4^{6}]

event b:[C(4,1) x C(6,2) x C(4,2) x C(2,1) x C(1,1) divided by 4^{6}]

And Since two events I showed above are mutually exclusive, I can do like this: a+b.

Is this the right procedure? Please check for me.

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# Homework Help: Combination problem help?

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