In a railway compartment, 8 seats are vacant on a bench. In how many ways can 5 passengers sit on them ?

Explanation

Number of vacant seats =8
Number of passengers =5
Number of ways for the first passenger to occypy seat=8
Number of ways for second passenger to occupy seat =8-1=7 (`therefore ` one has allready been occupied by the first passenger)
Number of ways for the third passenger to occupy seat =7-1=6
Following in the same manner the seat available for the last passenger is 4.
`therefore ` By the principle of multiplication, total number of ways for all five to occupy seats `=8xx7xx6xx5xx4=6720`