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In general, find the number of k-tuples  of nonnegative integers such that \(0 \le a_1 \le a_2 \le a_3 \le \dots \le a_k \le n.\)
 

 Feb 29, 2020
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\(\text{clearly all the $a$'s must be such that $0 \leq a_k \leq n$}\\ \text{given any set of $k$ integers there is exactly one unlabelled ordering of them satisfying above}\\ \text{so we can choose $k$ integers $0\leq a_k \leq n$ and sort them, and label them accordingly}\\ \text{there are $N=(n+1)^k$ different sets of $k$ integers in the range $[0,n]$}\)

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 Mar 1, 2020

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