1.      The global government of the planet Arthomid functions as a democracy with four major political parties, the Ansidro, the Kwoe, the Maclamarion, and the Troguat. The technology education committee of the government currently consists of 6 Ansidro, 9 Kwoe, 3 Maclamarion, and 4 Troguat and suppose that a 4-member subcommittee is formed for the purpose of studying the emotional response to new technologies in older adults.

-How many different subcommittees are possible?

-How many different subcommittees consist of at least 1 Ansidro?

-How many different subcommittees consist of exactly 2 Maclamarion and 1 Kwoe?

2.      An ARANDASPIS is a 6-in long extinct species of jawless fish from the Ordovician Period.

-In how many ways can the letters in ARANDASPIS be arranged?

-In how many different ways can the letters in ARANDASPIS be arranged if the first letter

must be an P and the last letter must be a A?

3.      Suppose that an exam has 32 questions on it and students need to answer 25 of the questions. In how many ways can this be done if the first 9 questions and exactly 5 of the last 6 questions must be answered, and question #17 must not be answered due to a typo?

4.      A 6-character password consists of two numbers (from 1 to 9) followed by four letters (from A to K).

-How many different passwords can be formed that have no repeated number or letters?

-How many different passwords can be formed if letters and numbers can be repeated?

5.      Suppose that an unfair coin comes up heads 55.8% of the time. The coin is flipped a total of 18 times.

-What is the probability that you get exactly 8 heads?

-What is the probability that you get at most 16 tails?

6.      A box contains 4 green, 6 red, 3 yellow, and 8 blue buttons. Four buttons are drawn from the box simultaneously.

-What is the probability that you get one button of each color?

-What is the probability that none of the buttons are red?

-What is the probability that at least three of the buttons are blue?

7.      Euchre is a card game that uses a 24-card deck (which can be formed by removing all of the

2’s, 3’s, 4’s, 5’s, 6’s, 7’s, and 8’s from a standard 52-card deck) in which the players are each dealt 5-card hands from the deck of 24. Suppose that you are playing Euchre and are dealt a 5-card hand. What is the probability that:

-You are dealt exactly 2 kings?

-You are dealt at least 1 diamond?

-How many different subcommittees are possible?

8.      A museum is in possession of 18 paintings by Andy Warhol and wishes to put 4 of them on display in its gallery. In how many ways can this be done if:

-The order in which the paintings are displayed matters?

-The order in which the paintings are displayed does not matter?

9.      Suppose that a game of chance is played with a pair of fair 8-sided dice (with the sides numbered 1 to 8). In the game, you can pick any number from 1 to 8 and the two dice are then “rolled” in a cage. If $1 is bet and exactly one of the number that you picked is rolled you win $1, and if both of the dice are the number that you picked you win $15 (in each of those cases you also get your initial $1 bet back). If none of your number winds up being rolled you lose your $1 bet. Suppose that you play this game 4 times and pick the same number each time.

-What is the probability that doubles of your number (both dice come up your number) does not occur in the 4 rolls?

-What is your total expected win or loss? Indicate in your answer both the amount (rounded to the nearest $0.01 if necessary) and whether it is a win or loss

10.  A bagel shop offers 21 varieties of bagels, 34 flavors of cream cheese, and 31 flavors of coffee. How many different orders for a bagel, cream cheese, and a coffee can a customer place?

11.  It is found that when a particular 6-sided die is rolled a 1 occurs 18.6% of the time, a 2 occurs 15.4% of the time, a 3 occurs 13.1% of the time, a 4 occurs 12.3% of the time, a 5 occurs 17.7% of the time, and a 6 occurs 22.9% of the time.

-If the die is rolled 8 times, what is the probability that an odd number occurs exactly 5 times?

-What is the expected value of a single roll of the die?

12.  For the die in problem #11, let the random variable X be defined as X = (the number of times that a 1 occurs). If the die is rolled a total of three times:

-Construct a table and histogram for the probability distribution of X.

-Find E(X).

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