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1) In a class of 30 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose to raise his or her hand. Eight hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 27 hands raised. How many students have piercings both on their ears and their noses?
2) The following problem refers to strings in A, B, …, Z.
How many three-letter strings are there that begin with H ?
3) How many different four-letter strings can be formed from the letters A, B, C, D, E (repeats allowed) if the first letter must be a consonant and the last letter must be a vowel?
4) There are 13 different pizza toppings, and Arturo must rank his top 4 in order. How many different possible rankings are there?
5) How many solutions (using only nonnegative integers) are there to the following equation?

x1 + x2 + x3 + x4 + x5 = 32
6) A restaurant offers three different kinds of soup and four different kinds of salad.

(a) If you are having either soup or salad, how many choices do you have?
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(b) If you are having both soup and salad, how many choices do you have?
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