HMMT 二月 2013 · 冲刺赛 · 第 4 题

HMMT February 2013 — Guts Round — Problem 4

[ 4 ] Spencer is making burritos, each of which consists of one wrap and one filling. He has enough filling for up to four beef burritos and three chicken burritos. However, he only has five wraps for the burritos; in how many orders can he make exactly five burritos? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT 2013, 16 FEBRUARY 2013 — GUTS ROUND Organization Team Team ID#

解析

[ 4 ] Spencer is making burritos, each of which consists of one wrap and one filling. He has enough filling for up to four beef burritos and three chicken burritos. However, he only has five wraps for the burritos; in how many orders can he make exactly five burritos? Answer: 25 Spencer’s burrito-making can include either 3, 2, or 1 chicken burrito; consequently, ( ) ( ) ( ) 5 5 5 he has + + = 25 orders in which he can make burritos. 3 2 1