Question

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

Answer 1

`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