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1. A group of people consists of 5 democrats, 7 republicans and 3 libertarians.

a) How many ways can they all line up so that members of the same party are together?

b) How many ways can they choose a committee of 2 members from each party?

2. In a raffle, 150 people each have one ticket. There are 1 first prize, 2 identical 2^nd prizes and 5 identical 3^rd prizes. How many ways can the prizes be awarded?

3. A box contains 8 red, 5 blue and 10 green balls. Four are chosen at random, without replacement. What is the probability of choosing

1. exactly 2 red or exactly 2 blue?

2. at least 1 red or at least 1 blue? Think complements.

4. A multiple choice test has 10 questions with 1 correct answer and 4 incorrect answers for each. If a person guesses randomly, what is the probability he will get at least 2 questions incorrect?

5. How many ways can a group of 100 people choose a subgroup consisting of 1 president, 1 vice president, 2 secretaries, and 3 financial planners? The two secretary positions are the same rank and the 3 financial planners are the same rank. You can count this in two ways, using the Mississippi formula or using a product of combinations. In the Mississippi formula approach, do not forget about the 93 people who get no assignment.

6. For each experiment; a) find n(S), b) list 4 outcomes in the event A, and c) find P(A)=n(A)/n(S).

I. Toss three six-sided dice and observe the top numbers. A is the event that the numbers 1, 2, and any other number (not 1 or 2) appear on top.

II. Toss three six sided dice and observe the top numbers. A is the event that exactly two ones appear on top.

III. Choose three cards all at once from a standard 52- card deck. A is the event that at most one heart is chosen.