Question

一名篮球运动员在一场比赛中投进了 $5$ 个球。每个进球值 $2$ 分或 $3$ 分。该运动员总得分可能有多少种不同的数值？

A basketball player made $5$ baskets during a game. Each basket was worth either $2$ or $3$ points. How many different numbers could represent the total points scored by the player?

$2$

$3$

$4$

$5$

$6$

答案：E

知识点：基本计数系统列举

难度评级：720

解答：

如果 $k$ 个进球值 $3$ 分，其余值 $2$ 分，总分为 $2(5-k)+3k=10+k$ 。

当 $k$ 取 $0,1,\ldots,5$ 时，总分取从 $10$ 到 $15$ 的每个整数，共 $6$ 种可能。

所以正确答案是 E。

If $k$ of the baskets are worth $3$ points and the rest worth $2,$ the total is $2(5-k)+3k=10+k.$

As $k$ ranges over $0,1,\ldots,5,$ the total takes every integer value from $10$ to $15,$ giving $6$ possibilities.

Thus, the correct answer is E.

2008 AMC 10B 第 1 题

答案：E

难度评级：720

解答：

其他年份的第 1 题