1. Cards are to be selected from an ordinary 52card 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 orii? 3. A club consists of ve 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? 4. How many distinguishable orderings of the letters of COMMENCEMENT don't have the three M's next to each other? 5. Find how many solutions there are to the given equation that satisfy the given condition. a + b + c = 30, each of a, b, and c is an integer that is at least 4