Question

Hi there, can you please answer A) and B), showing the working of the nCr formula too please. Also, please remember that it’s possible for the kids to have zero eggs, for part B).

thank you!

1. (4 marks) A basket contains eight green, seven yellow, and four purple eggs. (As- sume eggs of the same colour are indistinguishable.) These eggs are all handed out (a) How many ways can the eggs be distributed among the eight children, with (b) Let n be the largest number of eggs that any child receives. What is the range to a group of eight children no restriction on the number of eggs each child receives? of valucs that n can be? (Find the largest a and the smallest b that we can determine such that we are guaranteed a <n < b.)

Answer 1

a) There are four purple eggs which we want to distribute among eight children. Now 1^st egg can be distributed among eight children in 8_c_1 = 8 way similarly 2^nd egg can be distribute in 8 way. So In this way 4 egg can be distributed in 8 times 8 times 8 times 8 = 8^4 way = 4096 way b) Here one can get all the eggs and one does not get an egg. So the range of n is 0 lessthanorequalto n lessthanorequalto 4.