Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A town council is planning to plant 12 trees down the middle of a main road. The council purchases the trees from a garden centre that has 4 different hibiscus trees, 9 different jacaranda trees and 2 different oleander trees on sale.
(i)[4]
How many different selections of 12 trees can be made if there must be at least 2 of each tree type?
(ii)[3]
The council buys 4 hibiscus trees, 6 jacaranda trees and 2 oleander trees. In how many different arrangements can these 12 trees be made if the hibiscus trees must be together, the jacaranda trees must be together and the oleander trees must be together?
(iii)[3]
How many different arrangements of these 12 trees can be made if no hibiscus tree is beside another hibiscus tree?
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct combination such as $4C2\times9C8\times2C2$” …