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In how many ways can 7 people sit in a ROW?
A$7$
B$7^2 = 49$
C$\binom{7}{2} = 21$
D$7! = 5040$
Answer & Solution
Correct answer: D. $7! = 5040$
1. Number of arrangements of $n$ distinct people in a row: $n!$.
2. For 7 people: $7! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 5040$.
3. Other options ignore the multiplicative structure.
_Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §1.3 (Combinations and Permutations)._
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