mCr=m!/r!(m-r)! Property: mCr=mC(m-r) Example:

◦ If you have 10 pens, all in different colors, and you want to bring two of them to class, how many choices do you have?

Suppose you want to change the tires of your car and you don’t have to match them at all. If there are 6 brands of front tire and 5 brands of back tire, how many choices do you have?

At a poker game of 52 cards, every player gets five cards. What is the probability that you have at least one Ace in your hand?

What is the probability that you have a poker hand with two kings?

A manager has 17 employees that he needs to send to training. Each training session takes a week and he has to have everyone trained within three weeks. However, he can only send at most 6 people every week. How many different ways can he make this selection?

The U.S. senate consists of 100 senators, 2 from each state. A committee of 5 senators is to be formed.

A. How many different ways of forming this committee?

B. If no state can have more than one senator, then how many different ways?

At a sports event, there are 500 athletes and 100 judges. Finally, 10 people will be awarded for their good behavior.

A.How many different choices are there?B.If there must be both athlete and judges in

the 10 awarded, how many different choices?

Four people, including you, are playing a deck of 52 cards and each person gets 13 cards. Let X be the number of Aces you have. What is your sample space and what is the probability of each point in the sample space?

At a poker game, the dealer deals the 52 cards into four players. Each players will have 13 cards. What is the probability that one player has three suits at his hand?