How many combinations of three scoop cones are possibles?

Question

An ice cream shop sells ice creams in five possible flavours. How many combinations of three scoop cones are possibles?[Note:The repetition of flavours is allowed but the order in which the flavours are chosen does not matter.]

score 1 · Answer 1 · answered Jun 23 '14 at 04:15

To calculate choosing $n$ numbers with replacement you use, $$\binom{n+m-1}{m}$$

where $n$ in the total numbers in the set, and m is how many numbers you want to choose.

So, $$\binom{5+3-1}{3}=\binom{7}{3}=\frac{7\times 6\times 5}{1\times 2\times 3}=35$$

score 1 · Accepted Answer · answered Jun 23 '14 at 05:58

1

If I'm not mistaken, another solution (just to add flavor), would be:

$5\choose 1$ + $2$$5\choose 2$ + $5\choose 3$$=35$

answered Jun 23 '14 at 05:58

Vincent

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How many combinations of three scoop cones are possibles?

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