PUMaC 2013 · 组合（B 组） · 第 3 题

PUMaC 2013 — Combinatorics (Division B) — Problem 3

[ 4 ] Chris’s pet tiger travels by jumping north and east. Chris wants to ride his tiger from Fine Hall to McCosh, which is 3 jumps east and 10 jumps north. However, Chris wants to avoid the horde of PUMaC competitors eating lunch at Frist, located 2 jumps east and 4 jumps north of Fine Hall. How many ways can he get to McCosh without going through Frist?

解析

[ 4 ] Chris’s pet tiger travels by jumping north and east. Chris wants to ride his tiger from Fine Hall to McCosh, which is 3 jumps east and 10 jumps north. However, Chris wants to avoid the horde of PUMaC competitors eating lunch at Frist, located 2 jumps east and 4 jumps north of Fine Hall. How many ways can he get to McCosh without going through Frist? Solution There are 13 choose 3 ways to get to McCosh without the restriction, or 13 ∗ 11 ∗ 2 =
For Chris to avoid lunchers, he needs to not take a way through Frist; there are 6 choose 2, or 15, ways to Frist, and 7 choose 1, or 7, ways from it. This gives a total of 105 bad paths, for a final total of 181 paths to McCosh.