AMC / AIME · Stars and Bars · Easy

Stars and Bars: How many ways can math identical apples be split among math children (each may get zero)?

Integer solutions to linear equations.

Try the problem

How many ways can 77 identical apples be split among 33 children (each may get zero)?

Hint and answer

Concept to use

Nonnegative: $\binom{n+k-1}{k-1}$.

Hint

Nonnegative solutions to a+b+c=7a+b+c=7.

Answer

36

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