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## lgbasallote 3 years ago How many ways can you arrange four people in a row of four seats? is this 4P4?

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1. GOODMAN

No, its 4!

2. GOODMAN

4!= 4*3*2*1

3. sauravshakya

There is only one way

4. sauravshakya

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

5. lgbasallote

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

6. GOODMAN

So why go through all the trouble?

7. LolWolf

Yep, $$_4P_4$$ is correct.

8. lgbasallote

because of this next question im about to ask

9. lgbasallote

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

10. sauravshakya

Actually both will be 5!

11. sauravshakya

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

12. sauravshakya

If u are taking about arrangement

13. lgbasallote

....so they are both 5P4?

14. sauravshakya

Yep

15. sauravshakya

I think so

16. LolWolf

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".

17. lgbasallote

i think im getting the hang of this

18. LolWolf

Sounds good

19. karatechopper

So...like 16?

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