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Am I doing this correctly?

$C(r+n-1,n-1) = C(5+3-1,2) = \frac{7\times6}{1\times2} = 21$


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Yes.${}{}{}{}{}{}{}{}$ – André Nicolas Mar 2 '13 at 22:58
up vote 1 down vote accepted

When dealing with combinations (order doesn't matter) with repetition, you use this formula (where n = things to choose from and r = number of choices):


In your example problem you would then have n = 3, r = 5:

$\frac{(3+5-1)!}{5!(3-1)!} = \frac{7!}{5!2!} = \frac{7*6}{2*1} = 21$, so yes you are doing it right!

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