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 passengers will sit only in the lower deck and 8 passengers will sit in the upper deck.  Remaining passengers =20-(5+8)=7Seats remaining in lower deck=7−5=2 number of ways of filling 2 seats in the lower deck =C2   7=21Corresponding to each choice, the remaining  5=7–2 passengers will sit in the upper deck. number of choice =21