Answer:
The delivery driver can make deliveries at 5 locations among the remaining 6 locations using 6 different routes.
Step-by-step explanation:
To find the number of different routes the delivery driver can take to make deliveries at 5 locations among the remaining 6 locations, we can use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of locations, r is the number of locations the driver will visit, and ! denotes the factorial operation (e.g. 5! = 5 x 4 x 3 x 2 x 1).
In this case, we have:
n = 6 (the total number of locations)
r = 5 (the number of locations the driver will visit)
So, the number of different routes the driver can take is:
6C5 = 6! / 5!(6-5)! = 6
Therefore, the delivery driver can make deliveries at 5 locations among the remaining 6 locations using 6 different routes.
Combination formula:
The combination formula is used to calculate the number of ways we can select r items from a set of n items without regard to order. We use this formula when we want to count how many different groups of r items can be selected from a larger set of n items.
The formula is:
nCr = n! / r!(n-r)!
where:
n is the total number of items in the set
r is the number of items we want to select from the set
! denotes the factorial operation, which means we multiply all the whole numbers from 1 up to the given number.
Let's look at an example to see how it works.
Example:
Suppose we have a box of 10 colored balls: 4 red, 3 blue, and 3 green. We want to select 2 balls from the box, without regard to the order in which they are selected. How many different combinations of 2 balls can we choose?
Using the combination formula, we have:
n = 10 (the total number of balls)
r = 2 (the number of balls we want to select)
10C2 = 10! / 2!(10-2)! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (2 x 1 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 45
Therefore, there are 45 different combinations of 2 balls that can be selected from the box of 10 colored balls.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]