Answer:
So, there are 34,560 distinct arrangements of the letters in "REINTERPRET," accounting for the repeated letters.
Explanation:
To find the number of distinct arrangements of the 11 letters in "REINTERPRET" while treating the repeated letters as identical, we can use the concept of permutations.
First, let's determine the total number of arrangements if all the letters were distinct. Then, we'll account for the repeated letters.
Total number of letters = 11
If all letters were distinct, the number of arrangements would be 11!. However, since "R" appears twice, "E" appears three times, and "T" appears twice, we need to divide the result by the factorial of the number of times each letter is repeated.
So, the number of distinct arrangements is:
11! / (2! * 3! * 2!)
Calculating this:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
2! = 2 x 1 = 2
Now, divide 11! by the product of these factorials:
11! / (2! * 3! * 2!) = (11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (2 x 6 x 2) = 34,560
So, there are 34,560 distinct arrangements of the letters in "REINTERPRET," accounting for the repeated letters.