1 . A random sample of 330 people showed that 15 people liked Italian, Mexican, and Chinese food. The survey showed that 60 liked both Italian and Mexican, 75 liked both Italian and Chinese, and 100 liked both Mexican and Chinese food. Also, 210 people liked Mexican food, and 220 people liked Chinese food. If everyone liked one of the three, how many people liked only Italian?

2. Consider a list of randomly generated 4-letter "words" printed on a paper. The letters cannot be repeated.

(a) At least how many of these "words" should be printed to be sure of having at least 8 identical "words" on the list?

(b) At least how many identical "words" are printed if there are 3229201 "words"

on the list?

3. A computer is printing out subsets of a 4 element set (possibly including the empty set).

(a) At least how many sets must be printed to be sure of having at least 2 identical subsets on the list?

(b) At least how many identical subsets are printed if there are 49 subsets on the

list?