Find the number of distinct arrangements of the 10 letters in WOODWORKER.Two of the same letter are considered identical (not distinct).

To solve this problem, we use the formula for permutations of multiset: n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of item.

In the word "WOODWORKER", there are 10 letters in total.

The letter 'O' appears 3 times, 'W' appears 2 times, 'R' appears 2 times, and the letters 'D', 'K', and 'E' each appear 1 time.

So, we have:

n = 10 (total number of letters)

r1 = 3 (number of 'O's)

r2 = 2 (number of 'W's)

r3 = 2 (number of 'R's)

r4 = r5 = r6 = 1 (number of 'D', 'K', and 'E')

Substitute these values into the formula:

Number of distinct arrangements = 10! / (3! * 2! * 2! * 1! * 1! * 1!)

= 3,628,800 / (6 * 2 * 2 * 1 * 1 * 1)

= 3,628,800 / 24

= 151,200

So, there are 151,200 distinct arrangements of the letters in "WOODWORKER".