Question

There are 10 students in the class and 10 seats in the classroom, and each student sits in the same seat during every lesson, However, the teacher insists that no student sit in their "usual" seat during an exam. How many different seating arrangements are permissible during an exam?

Answer 1

there are 10!. !=factorial 10*9*8*7*6*5*4*3*2*1

Answer 2

I realize this is a derangement and I'll need to use

\[D _{n} = n!(1 -\frac{ 1 }{ 1! } + \frac{ 1 }{ 2! } - \frac{ 1 }{ 3! } + ...+(-1)^{n}\frac{ 1 }{ n! })\]
But I don't seem to be getting the correct answer.

Answer 3

Ah nevermind i did it wrong. this is a sequence

Answer 4

Pretty sure I will need to use that formula

Answer 5

yes you are 100% true

Answer 6

what course are you taking, didn't remember this in algebra, i did arithmetic and geometry ._.

Answer 7

discrete math

Answer 8

10!(1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6! - 1/7! + 1/8! - 1/9! + (-1)^10(1/(10!))

ok this might be right now, I'm getting 1334961

Answer 9

@dan815 Does this look right to you?

Answer 10

yes i got that

Answer 11

i had to get my tutor hehe

Answer 12

Haha, alright thanks.