MathDB

Problem Section #4
c) A special deck of cards contains

49

cards, each labeled with a number from

1

7

and colored with one of seven colors. Each number-color combination appears on exactly one card. John will select a set of eight cards from the deck at random. Given that he gets at least one card of each color and at least one card with each number, the probability that John can discard one of his cards and still have at least one card of each color and at least one card with each number is

\frac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p+q

Problem Statement