How many ways are there to choose ﬁve doughnuts if there are eight varieties (and only the type of each doughnut matters)?

Name: How many ways are there to choose ﬁve doughnuts if there are eight varieties (and only the type of each doughnut matters)?
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Question

Quizplus · Accepted Answer

The Answer is The number of diﬀerent ways to choose ﬁve doughnuts from eight diﬀerent varieties equals the number of 5-combinations with repetition allowed from a set with 8 elements. This equals

C ( 5 + 8 - 1,8 - 1 ) = C ( 12,7 ) = \frac { 12 ! } { 7 ! 5 ! } = \frac { 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 } { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 } = 792

How Many Ways Are There to Choose ﬁVe Doughnuts If