Competition problem — Combinatorics

Library / /27 of 520

Combinatorics Difficulty 5.3 AIME, harder Find the answer

5. Find the binomial coefficients $\binom{9}{3},\binom{9}{4}$ , and $\binom{10}{4}$ , and verify that $\binom{9}{3}+\binom{9}{4}=\binom{10}{4}$

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

5. $84,126,210$

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.