Distribution of candies among three children
Probability
Level
3
In how many ways can 20 identical candies be distributed among three children so that each gets at least one candy?
The answer is 171.
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1 solution
Suppose, 20 candies are to be distributed among A,b,c.
If we give 1 candy to a then remaining 19 candies can be distributed between b and c in 18 ways. If we give 2 candies to a then remaining 18 candies can be distributed between b and c in 17 ways
Similarly when a gets 18 candies there is only 1 way to distribute remaining 2 candies between b and c....
So total ways are 18+17+16+.....+1=171
Answer is 171 ways.