Question

A double-decker bus carry $(u+l)$ passengers, $u$ in the upperdeck and $l$ in the lower deck. The number of ways in which the $(u+l)$ passengers can be distributed in the two decks, if $r(\leq l)$ particular passengers refuse to go in the upper deck and $s(\leq u)$ refuse to sit in the lower deck, is/are

• A. ${ }^{u-s} C_{l-r}$
• B. $\frac{(u+l-r-s) !}{(l-r) !(u-s) !}$
• C. ${ }^{u-s} P_{l-r}$
• D. $\frac{(u+l) !}{r ! s !}$

Answer 1

Answer: (B)

Number of passengers to be allotted in two decker bus
$=(u+l)-(r+s)$
Number of seats available in the upper deck $=(u-s)$
$\therefore $ Total number of ways $=\frac{(u+l-r-s) !}{(l-r) !(u-s) !}$