Determine the number of permutations of the letter of the word "education"

To determine the number of permutations of the letters in the word "education," we can use the formula for permutations of a set of objects.

The word "education" contains 9 letters - 'e', 'd', 'u', 'c', 'a', 't', 'i', 'o', 'n'.

We can calculate the number of permutations using the formula:

n! / (n1! * n2! * .... nk!)

where n is the total number of objects (in this case, 9), and n1, n2, ..., nk are the number of times each object is repeated (if any).

In this case, there are no repeated letters in the word "education," so we can calculate the number of permutations as:

9! / (1! * 1! * 1! * 1! * 1! * 1! * 1! * 1! * 1!)

Simplifying this expression, we have:

9! / (1)

The factorial of 9 (denoted as 9!) is the product of all positive integers from 1 to 9:

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880

Therefore, the number of permutations of the letters in the word "education" is 362,880.

Since "education" can be written as

"acdeinotu" a nine letter word without repetition, the number of permutations is 9! = 362880