Find the number of distinct arrangements of the 11 letters in WOODWORKERS.Two of the same letter are considered identical (not distinct).

To find the number of distinct arrangements of the 11 letters in "WOODWORKERS", we can use the formula for permutations of a 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 "WOODWORKERS", there are 11 letters in total.

The letter 'O' appears 3 times, 'W' appears 2 times, 'R' appears 2 times, 'D' appears 1 time, 'K' appears 1 time, 'E' appears 1 time, and 'S' appears 1 time.

So, we can plug these values into the formula:

11! / (3! * 2! * 2! * 1! * 1! * 1! * 1!)

= 39,916,800 / (6 * 2 * 2 * 1 * 1 * 1 * 1)

= 39,916,800 / 24

= 1,663,200

So, there are 1,663,200 distinct arrangements of the 11 letters in "WOODWORKERS".