+6 1) There are 18 padded chairs around a circular table, and the chairs are numbered from 1 through 18 . How many ways can three people take their seats, so that no two people are adjacent?
2) Catherine rolls a 6-sided die five times, and the product of her rolls is 1200. How many different sequences of rolls could there have been? (The order of the rolls matters.)
1. There are 18*17*16 ways to choose the three seats, if people can be adjacent. We must subtract the cases where there are two people adjacent, which is 18*13*6. So the number of ways is 18*17*16 - 18*13*6 = 3492.
2. 1200 factors as 3*4*4*5*5. The number of rearrangements is 5!/(2!*2!) = 30.
