Question

If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

Memorize the first few factorials: $5! = 120$, $6! = 720$, $7! = 5040$. This saves calculation time during competitive exams.

Answer 1

The Correct Option is C

Step 1: What permutation of all means.
Arranging all $n$ different things in a row can be done in $n!$ ways. So we just need $n! = 5040$.

Step 2: Recall the factorial idea.
A factorial multiplies all whole numbers from 1 up to $n$. We test values until we hit 5040.

Step 3: Try small values.
$5! = 120$. Too small.

Step 4: Go higher.
$6! = 720$. Still too small.

Step 5: One more step.
$7! = 720 \times 7 = 5040$. That matches.

Step 6: Conclusion.
So the number of things is \[ \boxed{ n = 7 } \]