Using the letters in the word TRAMPOLINE, find the number of permutations that can be formed using 4 letters at a time. Show your work or explain how you got your answer. Using the formula nPr = n!/(n-r)!

Answer 1

In this case, we will be using the formula nPr = n! / (n - r)! to find the number of permutations.

First, let's determine the value of n and r. The word "TRAMPOLINE" has 10 letters, so n = 10. We want to choose 4 letters at a time, so r = 4.

Now we can plug these values into the formula:

nPr = 10! / (10 - 4)!
= 10! / 6!

To simplify this expression, we need to calculate 10! and 6!.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 3,628,800

6! = 6 x 5 x 4 x 3 x 2 x 1
= 720

Now we can substitute these values back into the formula:

nPr = 3,628,800 / 720
= 5,040

Therefore, there are 5,040 permutations that can be formed using 4 letters at a time from the word "TRAMPOLINE".