Question: You have 50 pennies and three jars, labeled A,B and C. How many ways can you put the pennies in the jars, assuming the pennies are identical.
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The number of ways to distribute r identical pennies into n different jars is $\displaystyle C(r+n-1,r)$ So, you have $\displaystyle C(50+3-1,50)$
There are $\displaystyle { {N+K-1} \choose {N}}$ ways to put N identical objects into K different cells.
Thanks for both answers.
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