Question: 1. A game consists of rolling ten dice, then choosing an integer falling between 7 and 21, inclusively. How many different outcomes are there to this game?
2. A man's outfit for the day consists of a pair of shoes, a pair of trousers, a shirt, tie, jacket, sweater (but not both), and coat and a hat. He has seven pairs of shoes, twelve pairs of trousers, fifteen shirts, ten ties, three jackets, four sweaters, two coats and four hats. How many different outfits are possible, assuming that all the pairings making up an outfit are compatible (so, for example, any shirt looks good with any sweater)?
3. How does the answer change, if at all, if an outfit consists of a pair of shoes, a pair of trousers, a shirt, tie, jacket and/or sweater, and a coat and/or hat?