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

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

The capacity of basket #1 is (b-3) eggs, of basket #2 is 2 eggs and of basket #3 is 1 eggs.

So we have a total of 'b' eggs.

In the case mentioned in the question above, b = 5

So, the number of different ways of putting these 'b' eggs in those three baskets is:

N = bCb-3*3C2

This is equivalent to:

N = bC3*3C2

For the case where b=5, the answer is:

N = 5C3*3C2 = 30

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.