3

Part of 2000 AIME Problems

Problems(2)

Binomial Expansion

Source:

In the expansion of

(ax+b)^{2000},

a

b

are relatively prime positive integers, the coefficients of

x^{2}

x^{3}

are equal. Find

a+b.

AIMEnumber theoryrelatively prime2000 AIME

Card Probability

Source:

A deck of forty cards consists of four 1's, four 2's,..., and four 10's. A matching pair (two cards with the same number) is removed from the deck. Given that these cards are not returned to the deck, let

m/n

be the probability that two randomly selected cards also form a pair, where

m

n

are relatively prime positive integers. Find

m+n.

probabilitynumber theoryrelatively prime