1. **State the problem:** We need to find the number of different possible arrangements (permutations) of the letters in the word "bookkeeper". 2. **Count the letters:** The word "bookkeeper" has 10 letters in total. 3. **Identify repeated letters:** - 'o' appears 2 times - 'k' appears 2 times - 'e' appears 3 times - 'b', 'p', 'r' each appear 1 time 4. **Use the formula for permutations of multiset:** $$\text{Number of arrangements} = \frac{10!}{2! \times 2! \times 3!}$$ 5. **Calculate factorials:** - $10! = 3628800$ - $2! = 2$ - $3! = 6$ 6. **Compute the denominator:** $$2! \times 2! \times 3! = 2 \times 2 \times 6 = 24$$ 7. **Calculate the number of arrangements:** $$\frac{3628800}{24} = 151200$$ **Final answer:** There are $151200$ different possible arrangements of the letters in "bookkeeper".