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Combinatorics

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Moderate

Musical Chairs

COMBIN-QKLLH1

A teacher has $n$ students in a class. Each day, the students sit in the same chairs as the previous days. For the final examination, the teacher asks that the students seat themselves in chairs so that no student sits in his or her usual chair.

If there are also $n$ seats in the class in how many ways may the students do this?

A

$\sum\limits_{i = 0}^n (-1)^i (n - i)!$

B

$\sum\limits_{i = 0}^n (-1)^i (n - i)^{n-i}$

C

$\sum\limits_{i = 0}^n (-1)^i {n \choose i}$

D

$\sum\limits_{i = 0}^n (-1)^i {n \choose i} (n - i)!$

E

$\sum\limits_{i = 0}^n (-1)^i {n \choose i} (n - i)^{n-i}$