20 passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. The number of ways that they can be distributed if 5 refuse to sit in the upper deck and 8 refuse to sit in the lower deck is

Passengers refusing to sit in the lower deck (resp. upper deck) will sit in the upper deck (resp. lower deck)
$5\text{ passengers will sit only in the lower deck and }8\text{ passengers will sit in the upper deck. }$$\text{ Remaining passengers }=20-(5+8)=7$Seats remaining in lower deck$=7-5=2$

$\text{ number of ways of filling }2\text{ seats in the lower deck }={}^7\mathrm{C}_2=21$
Corresponding to each choice, the remaining  $5\left(=7–2\right)$ passengers will sit in the upper deck.
 number of choice $=21$