Question

Amy and Adam are making boxes of truffles to give out as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?

• A. $12$
• B. $10$
• C. $15$
• D. $20$

Answer 1

The correct option is B $10$

10 boxes
In every combination, 2 types of truffles will be in the box, and 3 types of truffles will not. Therefore, this problem is a question about the number of anagrams that can be made from the "word" YYNNN:
$\frac{5!}{2!3!}=\frac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1\times 2\times 1}=5\times 2=10$