How many “words” can be formed using the letters of the word ARRANGEMENT?
11!/(2!2!2!2!) = 2,494,800
To find the number of "words" that can be formed using the letters of the word ARRANGEMENT, we can use the concept of permutations.
1. First, let's count the number of total letters in the word ARRANGEMENT. In this case, we have 11 letters.
2. Since the word contains repeating letters, we need to consider that as well. Here, we have 3 A's, 2 R's, and 2 N's.
3. Now, to calculate the number of "words," we can use the formula for permutations with repeating elements:
n! / (r1! * r2! * ... * rk!)
where n is the total number of letters and r1, r2, ..., rk are the frequencies of the repeating letters.
In our case, we can substitute the values:
11! / (3! * 2! * 2!)
4. Simplifying this expression, we get:
(11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1 * 1)
= 3991680 / 24
= 166,320
Therefore, there are 166,320 different "words" that can be formed using the letters of the word ARRANGEMENT.