Question

A​ golf-course architect has fivefive linden​ trees, fourfour white birch​ trees, and threethree 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?

Answer 1

Answer:

27,720 ways

Step-by-step explanation:

The number of permutations of non-distinct items is determined by the following expression:

$P = \frac{(N_1+N_2+N_3)!}{N_1!N_2!N_3!}$

If there are five linden​ trees, four white birch​ trees, and three bald cypress trees:

$P = \frac{(5+4+3)!}{5!4!3!}\\P=27,720\ ways$

The landscaper can plant the trees is 27,720 distinct ways.