How many “words” can be formed using the letters of the word ARRANGEMENT?
The letters:
AA
RR
NN
G
EE
M
T
Number of arrangements
= 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 utilize the concept of permutations.
The word ARRANGEMENT consists of 12 letters, including 3 A's, 2 R's, and 2 N's. The remaining letters are E, G, M, and T, each appearing once.
To calculate the total number of permutations, we need to consider that the same letters are repeated. The formula to find permutations is:
n! / (n1! * n2! * n3! ... nk!)
Where:
n is the total number of letters in the word (12),
n1, n2, ..., nk are the counts of each repeated letter.
Using this formula, we can calculate the number of "words" that can be formed using the letters of ARRANGEMENT:
12! / (3! * 2! * 2!)
= (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1 * 1)
= 39,916,800 / 12
= 3,326,400
Therefore, there are 3,326,400 distinct "words" that can be formed using the letters of the word ARRANGEMENT.