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SAM L.

asked • 09/20/20

A restaurant serves 10 different varieties of soup one of which is mushroom soup. In how many ways can we order six plates of soup if…

A restaurant serves 10 different varieties of soup one of which is mushroom soup. In how many ways can we order six plates of soup if (a) exactly four plates must be mushroom soup (b) at least four plates must be mushroom soup.

Based on my understanding, in this problem repetition is allowed and we have to apply combinations in distinguishable items. I applied the following formula: n+r-1Cr.

For number a, my answer is: (9+2-1)C(2-1)= 10. For number b, my answer is: (10+2-1)C(2-1) = 11. Did I get the correct answers?

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