AMC 8 1991 Problem 11

AMC8 1991 年第 11 题

排列与组合★★★☆☆

There are several sets of three different numbers whose sum is 15 which can be chosen from

\{ 1,2,3,4,5,6,7,8,9 \}

. How many of these sets contain a 5 ?

从

\{1,2,3,4,5,6,7,8,9\}

中可以选出几组三个不同数的集合，其和为 15？这些集合中有多少个包含 5？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Let the three-element set be

\{ a,b,c \}

and suppose that a=5.

We need b+c=10 and

b\neq c

. This gives us four solutions, so there are 4 sets with a 5 also with the desired properties

\rightarrow \text{B}

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