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1. Non-decreasing rolls of a die ●●●○○ 50 ptsA fair die is tossed 6 times. What is the probability that on each toss, the number shown is greater than or equal to the number on the previous toss? Give your answer as a decimal rounded to four decimal places.
2. Three piles of coins with increasing sizes ●●●○○ 50 ptsFind the number of ways $66$ identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile.