SOLUTION: there are 12 seat in a bus. how many ways can 10 people occupy them?

Question 862168: there are 12 seat in a bus. how many ways can 10 people occupy them?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula used would be the permutation formula of nPx.
n is the number of total seats on the bus.
x is the number of those seats you want to occupy at one time.
the formula for nPx is:
nPx = n! / (n-x)!
in your problem, n is equal to 12 and x is equal to 10.
the formula becomes:
12P10 = 12! / (12-10)! which is equal to 12! / 2! which is equal to 239,500,800.
the permutation formula is used because the seat that is assigned to each student can be different for each possible combination of 10 seats out of the 12.
for example:
1 combination of the seats could be seats 1,2,3,4,5,6,7,8,9,10
for that one combination of seats, the students in those seats could be arranged in 10! ways.
the permutation formula takes care of the total possible combination of seats and the position of the students within those seats.

RELATED QUESTIONS
There are six seat in a railway carriage. In how many different ways can 4 people occupy... (answered by ikleyn)

How many ways are there to seat 4 people in a row of 6... (answered by Edwin McCravy)

There are 12 people in a bus queue. Another 5 join them before 8 people get on a bus .... (answered by Fombitz)

There are four people lining up for a bus ride but only two of them are willing to take... (answered by stanbon)

In how many different ways can 12 people occupy the 12 seats in a front row of a mini... (answered by ikleyn)

In how many different ways can five people be seated on a five-seat bench if two of them... (answered by josmiceli)

five people enter a 12 seater bus. in how many ways can they be... (answered by ikleyn)

How many different ways are there to seat 20 people in 20 different... (answered by MathLover1)

How many ways can you seat 4 people in 10 different... (answered by stanbon)