Question

A​ golf-course architect has six 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? the trees can be planted in nothing different ways.

Answer 1

Total number of trees n = 4 + 3 + 3 = 10. Count the number of each different trees. n1=4, n2=3, n3=3. Number of ways the landscaper plant the trees in a row is = 10 ! / ( 4! * 3! * 3! ) = 3628800 / ( 24 * 6 * 6 ) = 3628800 / 864 = 4200 ways.

Therefore, the trees can be planted 4200 ways