1. Specials An ice cream parlor offers a special consisting of three scoops of ice cream chosen from 16 different flavors. Duplication of flavors is allowed. For instance, one possibility is two scoops of chocolate and one scoop of vanilla. Show that there are 816 different possible options for the special.
2. There are 6! = 720 six-letter words (that is, strings of letters) that can be made from the letters C, N, O, S, T, and U. If these 720 words are listed in alphabetical order, what position in the list will be occupied by TUCSON?
3. A five-digit ZIP code is said to be detour prone if it looks like a valid and different ZIP code when read upside down (Fig. 4). For instance, 68901 and 88111 are detour prone, whereas 32145 and 10801 are not. How many of the 105 possible ZIP code numbers are detour prone?

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PA. PRSRT STD U.S. POSTAGE PAID BETHLEHEM, PA PERMIT NO. 7470 18016 BE, BET