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
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