Question

A double-decker bus carry `(u+e)` passengers, `u` in the upper deck and `e` in the lower deck. Find the number of ways in which the `u+e` passengers can be distributed in the two decks, if `r(lt=e)` particular passengers refuse to go in the upper deck and `s(lt=u)` refuse to sit in the lower deck.

Answer 1

Correct Answer - `((u+l-r-s)!)/((l-r)!(u-s)!)`
Number of passengers to be allotted in the two decks bus
=(u+1)-(r+s)
Number of seats available in the upper deck
=u(u-s)
Number of seats available in lower deck =l-r
`therefore` Total number of ways of distribution `=((u+l-r-s)!)/((l-r)!(u-s)!)`