This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You can arrange the letters in the word BOOK in 12 distinct ways. 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