Question

How many ways can you arrange four people in a row of four seats?

is this 4P4?

Answer 1

No, its 4!

Answer 2

4!= 4*3*2*1

Answer 3

There is only one way

Answer 4

But If u are asking for different arrangement then its 4!

Answer 5

\[4 P 4 = \frac{4!}{(4-4)!} \implies \frac {4!}{0!} \implies 4!\]
@GOODMAN

Answer 6

So why go through all the trouble?

Answer 7

Yep, \(_4P_4\) is correct.

Answer 8

because of this next question im about to ask

Answer 9

what about for arranging 4 people in 5 seats? is that 5P4?

and arranging 5 people in 4 seats is also 5P4?

Answer 10

Actually both will be 5!

Answer 11

For first case it would be 5*4!=5!
For second case it would be 5*4*3*2 = 5!

Answer 12

If u are taking about arrangement

Answer 13

....so they are both 5P4?

Answer 14

Yep

Answer 15

I think so

Answer 16

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".

Answer 17

i think im getting the hang of this

Answer 18

Sounds good

Answer 19

So...like 16?