How many ways can 8 students be assigned a seat?

[Zelda22]

How many ways can 8 students be assigned a seat in a classroom if there are 10 seats in a row?

The first student can be assigned a seat = 10 ways
1 seat is now occupied, next student has 9 seats to sit

The second student can be assigned a seat = 9 ways
2 seats are now occupied, next student has 8 seats to sit

The third student can be assigned a seat = 8 ways
3 seats are now occupied, next student has 7 seats to sit

The fourth student can be assigned a seat = 7 ways
4 seats are now occupied, next student has 6 seats to sit

The fifth student can be assigned a seat = 6 ways
5 seats are now occupied, next student has 5 seats to sit

The sixth student can be assigned a seat = 5 ways
6 seats are now occupied, next student has 4 seats to sit

The seventh student can be assigned a seat = 4 ways
7 seats are now occupied, next student has 3 seats to sit

The last student can be assigned a seat = 3 ways

8 students can be assigned a seat in a classroom =10*9*8*7*6*5*4*3 = 1,814,400 ways

Is my reasoning correct? Thanks

 

[Steven G]

Looks good to me.

You can test your method with 2 students in 4 seats and get an idea if your method will work.

 

[BigBeachBanana]

How many ways can 8 students be assigned a seat in a classroom if there are 10 seats in a row?

The first student can be assigned a seat = 10 ways
1 seat is now occupied, next student has 9 seats to sit

The second student can be assigned a seat = 9 ways
2 seats are now occupied, next student has 8 seats to sit

The third student can be assigned a seat = 8 ways
3 seats are now occupied, next student has 7 seats to sit

The fourth student can be assigned a seat = 7 ways
4 seats are now occupied, next student has 6 seats to sit

The fifth student can be assigned a seat = 6 ways
5 seats are now occupied, next student has 5 seats to sit

The sixth student can be assigned a seat = 5 ways
6 seats are now occupied, next student has 4 seats to sit

The seventh student can be assigned a seat = 4 ways
7 seats are now occupied, next student has 3 seats to sit

The last student can be assigned a seat = 3 ways

8 students can be assigned a seat in a classroom =10*9*8*7*6*5*4*3 = 1,814,400 ways

Is my reasoning correct? Thanks

Or if you learned about counting with permutation, it's equivalent to
[math]\large_{10}P_{8}= \frac{10!}{(10-8)!}[/math]

 

[Zelda22]

Or if you learned about counting with permutation, it's equivalent to
[math]\large_{10}P_{8}= \frac{10!}{(10-8)!}[/math]

Looks good to me.

You can test your method with 2 students in 4 seats and get an idea if your method will work.

Thank you.

 

[Zelda22]

Or if you learned about counting with permutation, it's equivalent to
[math]\large_{10}P_{8}= \frac{10!}{(10-8)!}[/math]

Thank you. I started to learn permutations and combinations (after you guys mentioned them here), but I get confused about which one should I use.