# MATHEMATICS

Here are some sample questions:

1.    How many ways are there to rearrange the letters in FUNCTION?

2.    How many ways are there to rearrange the letters in INANENESS?

3.    Refer to Example 4.40. An urn contains nine red balls, nine white balls, and nine blue balls, and sample of four balls is drawn at random without replacement.

Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

4.    In a suitable font, the letters A, H, I, M, O, T, U, V, W, X, Y are all mirror images of themselves. A string made from these letters will be a mirror image of itself if it reads the same backward as forward: for example, MOM, YUMMUY, MOTHTOM. If a four-letter string in these letters is chosen at random, what is the probability that this string is a mirror image of itself? (Round your answer to four decimal places.)

5.    An urn contains six red balls, five white balls, and four black balls. Three balls are drawn from the urn at random without replacement. For each red ball drawn, you win \$4, and for each black ball drawn, you lose \$6. Let X represent your net winnings.

Compute E(X), your expected net winnings.

E(X) =

5.      Write a recursive function in pseudocode that computes the value of the following recurrence relation:

H(n) =

 1 if n = 1 H(n − 1) + 6n − 6 if n > 1.

Give descriptive preconditions and postconditions.

 precondition n       [removed] postcondition H(n) =

6.      Consider the following pseudocode function.

 function W() if n > 0 then if n is odd then return 2n else return n + 1 else return n − 1

Compute the values returned by the following function calls.

(a)    W(12) = [removed]

(b)    W(−19) = [removed]

(c)    W(7) = [removed]

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