A bakery sells 6 different varieties of cupcakes (chocolate, vanilla, red velvet, etc.). How many ways are there to fill a box with 24 cupcakes from the 6 varieties? The order in which the cupcakes are selected is unimportant; all that matters is the number of each variety in the box after they are chosen.

Question

Business

Nathalia Glass

3 October, 11:21

A bakery sells 6 different varieties of cupcakes (chocolate, vanilla, red velvet, etc.). How many ways are there to fill a box with 24 cupcakes from the 6 varieties? The order in which the cupcakes are selected is unimportant; all that matters is the number of each variety in the box after they are chosen.

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Answers (1)

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Emiliano Cross · Answer 1

118755

Explanation:

Here let x1, x2, x3 ..., x6 are number of cupcakes from each variety;

Therefore x1+x2+x3+x4+x5+x6 = 24

Since the order in which the cupcakes are selected is unimportant we have the following;

Number of non-negative solution of above equation = 24+6-1C6-1 = 29C5 = 118755

Therefore the correct answer is 118755