Question

12 of 14 (10 complete) HW Score: 71.439 Score: 0 of 1 pt Quest 5.5.57 A golf-course architect has four linden trees, four white birch trees, and three bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced? different ways The trees can be planted in Enter your answer in the answer box and then click Check Answer. Check Ana Clear All All parts showing SAMSUNG

Answer 1

First of all assume that all the trees of any kind are equally likely. That means all the 4 linden trees are identical all 4 white birch trees are identical and 3 bald Cypress are identical.

Then we have total 4+4+3 = 11 trees.

So 11 trees can be arranged in 11! Ways.. but all the trees are not different. There is some identical trees. So we have to divide the number of such arrangements of the identical trees from 11! . Which is 4!4!3!

So the number of different ways to plant the trees in a row is = $\frac{11!}{4!4!3!}$ = 11550 .