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Probability Sums

5 distinct numbers are chosen at random from {1,2,3,4,5,6,7,8,9}.

p(k) = probability their sum = k.

What are some of the ways you can find this in general?
What sum is/are the least likely?
Which sum is/are most likely?

p(15)=?

p(35)=?


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James Tanton
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