Question 2

Thirty volunteers are distributed to three polling booths. Each booth must have at least one and all must have different number of volunteers allotted. Then the number of ways of allocating volunteers is

Solution

Let the three numbers of volunteers be $$x<y<z$$, so $$x+y+z=30$$. The possible ordered triples are counted by considering the possible values of the smallest number, giving $$61$$ unordered triples. Since the three booths are distinct, each triple can be assigned in $$3!=6$$ ways, giving $$61\times6=366$$. Therefore none of the listed numerical choices is correct.

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Thirty volunteers are distributed to three polling booths. Each booth must have at least one and all must have different number of volunteers allotted. Then the number of ways of allocating volunteers is

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