Find the number of distinct arrangements of the 12 letters in REENGINEERED.Two of the same letter are considered identical (not distinct).
Question
Find the number of distinct arrangements of the 12 letters in REENGINEERED.
Two of the same letter are considered identical (not distinct).
Solution
To solve this problem, we will use the formula for permutations of a multiset. This formula is n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of item.
In the word "REENGINEERED", there are 12 letters in total.
There are 5 'E's, 3 'R's, 2 'N's, 1 'G', and 1 'D'.
So, n = 12, r1 = 5 (for 'E'), r2 = 3 (for 'R'), r3 = 2 (for 'N'), r4 = 1 (for 'G'), and r5 = 1 (for 'D').
Substituting these values into the formula gives us:
12! / (5! * 3! * 2! * 1! * 1!) = 39,916,800 / (120 * 6 * 2 * 1 * 1) = 39,916,800 / 1440 = 27,720
So, there are 27,720 distinct arrangements of the letters in "REENGINEERED".
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