How many permutations of the letters of the word APPLE are there?

To find the number of permutations of the letters in the word APPLE, we can use the formula for permutations of a set with repeated elements.

Step 1: Count the number of times each letter appears in the word APPLE. In this case, we have 1 A, 2 P's, 1 L, and 1 E.

Step 2: Calculate the factorial of the total number of letters in the word. In this case, we have 5 letters, so the factorial is 5!.

Step 3: Divide the factorial by the factorial of the number of times each letter appears. In this case, we divide 5! by 1! (for the A), 2! (for the P's), 1! (for the L), and 1! (for the E).

Step 4: Simplify the expression.

5! / (1! * 2! * 1! * 1!) = 5 * 4 * 3 * 2 * 1 / (1 * 2 * 1 * 1) = 5 * 4 * 3 = 60

Therefore, there are 60 permutations of the letters in the word APPLE.