A basket contains eight green, seven yellow, and four purple eggs. (Assume eggs of the same colour are indistinguishable.) These eggs are all handed out to a group of eight children.
(a)How many ways can the eggs be distributed among the eight children, with no restriction on the number of eggs each child receives?
(b)Let n be the largest number of eggs that any child receives. What is the range of values that n can be? (Find the largest a and the smallest b that we can determine such that we are guaranteed $a ≤ n ≤ b$.)
So I am trying to figure this question out. There are a total of 19 eggs, with 3 colours. The eggs of the same colour are indistinguishable - so this means that the orders won't matter. But how would I construct a combination for this? I have been stuck on this question for a while and I have no progress. Any hints will be appreciated.
For (b), since there are 19 eggs, would the largest be $11$ and the smallest be 1, so $1 ≤ n ≤ 11$?
They wanted $a$ to be the largest value but it is on the left side of $n$...