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

### Concept & Logic When a word consists of $n$ distinct letters, the number of ways they can be arranged in a line is given by $n!$ (n factorial). $$P = n!$$ ### Step-by-Step Solution - **Given:** The word 'DISPLAY'. - Count the total number of letters: D, I, S, P, L, A, Y. There are $7$ letters. - Check for repetition: All letters in the word are perfectly distinct from one another. - Calculate the total permutations: $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$. - Multiplication yields $5040$. ### Exam Strategy & Shortcut Memorize the factorials up to $7!$ (where $5!=120$, $6!=720$, $7!=5040$). Recognizing the word length immediately yields the answer without requiring manual multiplication on paper. ### Common Pitfall Miscounting the number of letters in the word or accidentally skipping a digit when multiplying the factorial sequence out manually. ### Final Answer Therefore, the correct answer is **5040**.