In how many different ways can the letters of the word 'BAKERY' be arranged?

### Concept & Basic Permutation The number of ways to arrange $n$ distinct objects in a sequence is simply $n$ factorial, denoted as $n!$. $$ n! = n \times (n-1) \times (n-2) \times \dots \times 1 $$ ### Step-by-Step Solution * **Analyze the Word:** The word "BAKERY" consists of the letters B, A, K, E, R, Y. * **Count the Letters:** There are 6 letters in total. * **Check for Repetitions:** All letters are completely distinct (no letter appears more than once). * **Calculate Arrangements:** Since there are 6 distinct letters, the total number of permutations is $6!$. * $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$. ### Exam Strategy & Shortcut Factorial memorization is non-negotiable for competitive exams. You should instantly know that $5! = 120$, $6! = 720$, and $7! = 5040$. This turns a calculation problem into a simple recall problem, taking less than 2 seconds. ### Common Pitfall Checking for repeating letters is a mandatory first step. If a student assumes all letters are distinct without checking and uses $n!$, they will get the wrong answer on words like "BANANA". Fortunately, BAKERY has no repeats, so the basic formula applies safely. ### Final Answer Therefore, the correct answer is **720**.