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How many compositions does 40 have (with up to 5 addends), with each positive integer addend between 2 and 12?
I was on Youtube and found a show called Monopoly Millionaires' Club. I thought it would be interesting to try to calculate the probability of winning the million dollars.
The contestant starts on ...
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Generating function for partitions into parts
My question is short and (maybe) simple: What is the generating function for partitions into distinct parts equal to $2, 5$ or $7$?
My idea is to use Euler's theorem: $$\sum p(k)x^k=\prod\frac{1}{1-...
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Count the number of ways n different-sided dice can add up to a given number
I am trying to find a way to count the number of ways n different-sided dice can add up to a given number.
For example, 2 dice, 4- and 6-sided, can add up to 8 in 3 different ways: ($(2,6),(3,5),(4,4)...
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