(10%) Basket #1 holds (b-3) eggs; basket #2 holds 2 eggs; and basket #3 holds 1

Question

(10%) Basket #1 holds (b-3) eggs; basket #2 holds 2 eggs; and basket #3 holds 1 egg. In how many ways, exactly, can b eggs be sorted into the baskets? (For example, if b = 5 and the eggs are labeled E1, E2, E3, E4, E5, then one way of sorting the eggs would be {E1 & E2} in basket #1, {E3 & E4} in basket #2, and {E5} in basket #3. This is no different from the sorting {E2 & E1} in basket #1, {E3 & E4} in basket #2, and {E5} in basket #3. But it is different from {E3 & E4} in basket #1, {E1 & E2} in basket #2, and {E5} in basket #3.

Explanation / Answer

There r b ways of placing eggs in basket 3

From the remaining b-1 eggs, we can chose 2 eggs in (b-1)(b-2)/2 ways (combination of 2 from (b-1) options)

The rest of the eggs will go to basket 1

So, the total ways possible = b x (b-1) x (b-2)/2 ways

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