The nurseryman brought six different varieties of trees to plant in six locations in the park. In how many different ways can he plant the trees
To find the number of different ways the nurseryman can plant the trees, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.
In this case, there are six varieties of trees and six locations. Since each tree must be planted in a different location, we have a one-to-one correspondence between the trees and the locations.
To calculate the number of possible arrangements, we can use the formula for permutations of n objects taken r at a time:
P(n, r) = n! / (n - r)!
Where n is the total number of objects (varieties of trees) and r is the number of objects to be selected (locations).
In this case, n = 6 (six varieties of trees) and r = 6 (six locations). Substituting these values into the formula:
P(6, 6) = 6! / (6 - 6)!
= 6! / 0!
= 6! / 1
= 6!
Since 0! = 1, we have:
6! = 6 x 5 x 4 x 3 x 2 x 1
= 720
Therefore, there are 720 different ways the nurseryman can plant the trees in the park.