How many ways can you arrange four people in a row of four seats? is this 4P4?

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How many ways can you arrange four people in a row of four seats? is this 4P4?

Mathematics
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No, its 4!
4!= 4*3*2*1
There is only one way

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Other answers:

But If u are asking for different arrangement then its 4!
\[4 P 4 = \frac{4!}{(4-4)!} \implies \frac {4!}{0!} \implies 4!\] @GOODMAN
So why go through all the trouble?
Yep, \(_4P_4\) is correct.
because of this next question im about to ask
what about for arranging 4 people in 5 seats? is that 5P4? and arranging 5 people in 4 seats is also 5P4?
Actually both will be 5!
For first case it would be 5*4!=5! For second case it would be 5*4*3*2 = 5!
If u are taking about arrangement
....so they are both 5P4?
Yep
I think so
Yes to both responses. To check we can show that: 4 people in 5 seats: We can always choose a single person whom is not in a seat, and there are 5 ways to do this, while the remaining 4 get a seat, thus: \(5\cdot_4P_4= _5P_4\), while for the latter, we have, simply \(_5P_4\) as the definition of "permute".
i think im getting the hang of this
Sounds good
So...like 16?

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