Question:
If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$
If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$
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Memorize the first few factorials: $5! = 120$, $6! = 720$, $7! = 5040$. This saves calculation time during competitive exams.
Updated On: May 31, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Concept
The number of permutations of $n$ distinct objects taken all at a time is given by $n!$ (n-factorial).
Step 2: Meaning
We are given that $n! = 5040$, and we need to find the value of the positive integer $n$.
Step 3: Analysis
Let us compute factorials of consecutive integers:
• $5! = 120$
• $6! = 720$
• $7! = 720 \times 7 = 5040$ Thus, $n$ must equal $7$.
Step 4: Conclusion
The value of $n$ is $7$ because $7!$ equals $5040$. Final Answer: (C)
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