PUMaC 2013 · 组合（B 组） · 第 7 题

PUMaC 2013 — Combinatorics (Division B) — Problem 7

[ 7 ] You are eating at a fancy restaurant with a person you wish to impress. For some reason, you think that eating at least one spicy course and one meat-filled course will impress the person. The meal is five courses, with four options for each course. Each course has one option that is spicy and meat-filled, one option that is just spicy, one that is just meat-filled, and one that is neither spicy nor meat-filled. How many possible meals can you have?

解析

[ 7 ] You are eating at a fancy restaurant with a person you wish to impress. For some reason, you think that eating at least one spicy course and one meat-filled course will impress the person. The meal is five courses, with four options for each course. Each course has one option that is spicy and meat-filled, one option that is just spicy, one that is just meat-filled, and one that is neither spicy nor meat-filled. How many possible meals can you have? 5 5 Solution Inclusion exclusion: there are 4 meals if we ignore requirements. There are 2 that 5 5 5 avoid spice, 2 that avoid meat, and one that avoids both, for 4 − 2(2 ) + 1 = 961 total meals.