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Alexander Clifton visits Sweet Dreams bakery, which sells three kinds of cookies. How many unique assortments of a dozen cookies can Alexander buy?

A. 1
B. 3
C. 6
D. 12

User DivineChef
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1 Answer

2 votes

Final answer:

The unique assortments of a dozen cookies Alexander can buy from a bakery that sells three kinds of cookies are 91, calculated using the formula for combinations with repetitions.

Step-by-step explanation:

The question revolves around the concept of combinations and how many unique assortments of a dozen cookies Alexander can buy if Sweet Dreams bakery sells three kinds of cookies. To solve, we treat this as a problem of distributing 12 identical items (cookies) into 3 unique categories (types of cookies). This can be solved using the formula for combinations with repetitions, which is:

(n + k - 1)! / (k!(n - 1)!)

Where n is the number of types of cookies, and k is the number of cookies being chosen. In this case, n = 3 and k = 12.

Applying the formula we get:

(3 + 12 - 1)! / (12!(3 - 1)!) = 14! / (12!2!) = 91.

Therefore, the answer is not listed among the available options A-D, since there are 91 unique assortments possible instead of 1, 3, 6, or 12.

User Meeti Sharma
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