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.
To find the number of permutations that can be formed using 4 letters at a time from the word TRAMPOLINE, we first need to determine the number of ways we can choose 4 letters from the 10 letters in the word.
This can be calculated using the combination formula, which is:
nCr = n! / r!(n-r)!
Where n represents the total number of items, and r represents the number of items to be chosen at a time.
In this case, n = 10 (the number of letters in TRAMPOLINE) and r = 4 (the number of letters we want to choose at a time).
Plugging these values into the formula:
10C4 = 10! / 4!(10-4)!
Calculating the factorials:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800
4! = 4 * 3 * 2 * 1 = 24
(10-4)! = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Replacing these values in the formula:
10C4 = 3628800 / (24 * 720) = 210.
Therefore, there are 210 permutations that can be formed using 4 letters at a time from the word TRAMPOLINE.