alleryThe number of ways to arrange $n$ distinct objects in a row is:
A$2^n$
B$n$
C$n!$
D$n^2$
Answer & Solution
Correct answer: C. $n!$
Arrangements of $n$ distinct objects in a row: $n$ choices for the first position
then $n-1$ for the second, $n-2$ for the third, etc. By the multiplication principle:
$n \times (n-1) \times \ldots \times 1 = n!$
For 5 books on a shelf: $5! = 120$ arrangements. For 10 students in a line: $10! = 3,628,800$.
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