Question

How many distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins?

Answer 1

Hi there!
Here's the answer:

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There are Distinct ways to split 50 identical coins among 3 people so that each person may get atleast Monroe coin

First 5 coins will be distributed among the 3 randomly

(x1 + 5) + (x2 + 5) + (x3 + 5) = 50
=> x1 + x2 + x3 = 35.

Now distribute remaining 35 coins to 3 people randomly

No. of ways of distributing 35 coins to 3 people randomly = $(35+3-1)_{C}__{3-1}$

= $37_{C}__{2}$

= 666.



^^^ Here the formula, $(n+r-1)_{C}__{r-1}$ is used to distribute ' r' identical(indistinguishable) objects among 'n' members.

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