1. Cards are to be selected from an ordinary 52-card deck. (a) How many cards must be selected to be sure of getting at least 3 cards from one suit? (b) How many cards must be selected to be sure of getting at least 3 diamonds? 2. How many integers from 1 through 500 must you pick in order to be sure of getting one that is divisible by 5 or 117 3. A club consists of five men and seven women. A committee of six is to be chosen. (a) How many committees of six contain three men and three women? (b) How many committees of six contain at least two men?