Four persons enter a railway carriage in which there are six seats, in how many ways can they take their place?

1 Answer
Jan 31, 2018

360 ways

Explanation:

The 1st person can sit in =6 seats
the 2nd person can sit in =5 seats (because 1 seat is already taken)
The 3rd person can sit in = 4 seats
The 4th person can sit in 3 seats

So they can sit in = (6!)/(2!) = 360 ways

or, the other way is:

4 seats can be chosen from 6 seats in 6C4 ways
and 4 people can be arranged in 4! ways

Therefore, total ways of seating = 6C4 xx 4!

= (6!)/((2!)xx(4!)) xx4! = 360 ways