How many ways can you arrange the letters in the word BOOK?

Here's how to calculate it:

1. Count the total number of letters: The word BOOK has 4 letters.

2. Identify repeated letters: The letter 'O' appears 2 times.

3. Use the permutation formula for repetitions: The number of distinct permutations of n objects where there are n1 identical objects of type 1, n2 identical objects of type 2, and so on, is given by n! / (n1! * n2! * ...).

   In this case:

   • n = 4 (total letters)
   • n_O = 2 (number of times 'O' is repeated)
   • n_B = 1 (number of times 'B' appears)
   • n_K = 1 (number of times 'K' appears)

   Number of arrangements = 4! / (2! * 1! * 1!)
   = (4 × 3 × 2 × 1) / ((2 × 1) × 1 × 1)
   = 24 / 2
   = 12