AMC8 1991

AMC8 1991 · Q11

AMC8 1991 · Q11. It mainly tests Basic counting (rules of product/sum), Casework.

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?

从集合$\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$中可以选择若干个不同数字之和为15的三元组集合。其中包含5的集合有多少个？

(A) 3 3

(B) 4 4

(D) 6 6

(E) 7 7

Answer

Correct choice: (B)

正确答案：（B）

Solution

After the 5 is selected, a sum of 10 is needed. There are four pairs that yield 10: 9+1, 8+2, 7+3, 6+4. Thus there are four 3-element subsets which include 5 and whose sum is 15.

选定5后，还需和为10。有四个数对和为10：9+1、8+2、7+3、6+4。因此包含5且和为15的三元子集有四个。

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