Problem

With a short time remaining in the day, a delivery driver has time to make deliveries at 6 locations among the 7 locations remaining. How many different routes are possible?
There are possible different routes.
(Simplify your answer.)

Answer

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Answer

\(\boxed{7}\) is the final answer, meaning there are 7 different routes possible for the driver.

Steps

Step 1 :This problem is about finding the number of different routes a delivery driver can take. The driver has time to make deliveries at 6 locations among the 7 locations remaining.

Step 2 :This is a combination problem because the order of the locations does not matter. We use the combination formula which is nCr = n! / r!(n-r)!. Here, n is the total number of locations (7) and r is the number of locations the driver can visit (6).

Step 3 :Substituting the values into the formula, we get 7C6 = 7! / 6!(7-6)!. Simplifying this, we find that there are 7 different routes possible.

Step 4 :\(\boxed{7}\) is the final answer, meaning there are 7 different routes possible for the driver.

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