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
Let's solve this problem about permutations. To find the number of ways the word "hell" can be permuted such that the L's are always apart, we can use the following method: Step 1: Calculate the total number of permutations of the word "hell". The word "hell" has 4 letters: H, E, L, L. There are 4 letters in total, with the letter 'L' repeated 2 times. The formula for permutations with repeated items is n! / (p₁! × p₂! × ...), where n is the total number of items and p₁, p₂, ... are the counts of repeated items. Total permutations = 4! / 2! = (4 × 3 × 2 × 1) / (2 × 1) = 24 / 2 = 12 Step 2: Calculate the number of permutations where the L's are together. To do this, treat the two 'L's as a single block (LL). Now we are permuting 3 items: (LL), H, E. Since these 3 items are distinct, the number of permutations is 3!. Permutations with L's together = 3! = 3 × 2 × 1 = 6 Step 3: Subtract the permutations where L's are together from the total permutations to find where the L's are apart. Number of permutations with L's apart = Total permutations - Permutations with L's together = 12 - 6 = 6 There are 6 ways to permute the word "hell" such that the L's are always apart. What's next? 📸