How many different ways can the letters of "personnel" be arranged? If the letters of "personnel" are arranged in a random order, what is the probability that the result will be "personnel"? The number of different ways that the letters of "personnel" can be arranged is (Type an integer or a simplified fraction.) The probability that the random arrangement of letters will result in "personnel" is (Type an integer or a simplified fraction.)

Step 1 ：The first part of the question asks for the number of different ways the letters of 'personnel' can be arranged. This is a permutation problem with repetition. The formula for permutations with repetition is \(\frac{n!}{r1!r2!...rn!}\), where n is the total number of items, and r1, r2, ..., rn are the numbers of each type of repetitive items. In this case, n is 9 (the number of letters in 'personnel'), r1 is 2 (the number of 'p's), r2 is 2 (the number of 'e's), r3 is 2 (the number of 'o's), and r4 is 2 (the number of 'n's).

Step 2 ：Using the formula, we find that the total number of arrangements is 22680.

Step 3 ：The second part of the question asks for the probability that a random arrangement of the letters will result in 'personnel'. This is simply 1 divided by the total number of arrangements, since 'personnel' is one specific arrangement out of all possible arrangements.

Step 4 ：Using this information, we find that the probability is \(\frac{1}{22680}\).

Step 5 ：Final Answer: The number of different ways that the letters of 'personnel' can be arranged is \(\boxed{22680}\). The probability that the random arrangement of letters will result in 'personnel' is \(\boxed{\frac{1}{22680}}\).