SOLUTION: How many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row?

Question 519221: How many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
First Student can be assigned a seat = 10 ways
Since the 1 seat is occupied next student has 9 seats to sit
Second Student can be assigned a seat = 9 ways
Since the 2 seats are occupied next student has 8 seats to sit
Third Student can be assigned a seat = 8 ways
Since the 3 seats are occupied next student has 7 seats to sit
Fourth Student can be assigned a seat = 7 ways
Since the 4 seats are occupied next student has 6 seats to sit
Fifth Student can be assigned a seat = 6 ways
Since the 5 seats are occupied next student has 5 seats to sit
Sixth Student can be assigned a seat = 5 ways
Since the 6 seats are occupied next student has 4 seats to sit
Seventh Student can be assigned a seat = 4 ways
7 students can be assigned a seat in a classroom =10*9*8*7*5*4=604800 ways
It is a case of choosing 7 out of 10
nPr=n!/(n-r)!
10P7=10!/(10-7)!
10P7=10!/3!
10P7=10*8*7*6*5*4*3!/3!
Cancel out 3!
10P7=10*9*8*7*6*5*4=604800 ways

RELATED QUESTIONS
how many ways can 5 students be assigned a seat in a classroom if there are 7 seats in a... (answered by Fombitz)

How many ways can 3 students be assigned a seat in a classroom if there are 11 seats in a (answered by edjones)

In how many ways can 4 students be seated in a classroom if there are 7 available seats? (answered by ikleyn)

If 5 students are all sitting in a row of seats, In how many different ways can they seat (answered by ewatrrr)

There are two rows of seats in the classroom and each row has six seats. If a class has... (answered by Boreal)

There are two rows of seats in the classroom and each row has six seats. If a class has... (answered by Edwin McCravy)

There are 7 students in a class. If there are 3 seats in the front row, how many ways can (answered by josmiceli,ikleyn)

In how many ways can 7 students be assigned seats in a row containing 7 desks if two of... (answered by varun)

In how many different ways can 6 students be assigned to 6 seats that are arranged: In a (answered by richard1234)