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.

Question

Mathematics

Boomhauer

23 April, 06:22

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.

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Max Tyler · 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