Exam-Style Problem

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June 2013 p62 q6
2787

A town council plans to plant 12 trees along the centre of a main road. The council buys 4 hibiscus trees, 6 jacaranda trees and 2 oleander trees.

(ii) How many different arrangements of these 12 trees can be made if the hibiscus trees have to be next to each other, the jacaranda trees have to be next to each other and the oleander trees have to be next to each other?

(iii) How many different arrangements of these 12 trees can be made if no hibiscus tree is next to another hibiscus tree?

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