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Question: A double-decker bus carry (u +l) passengers, u in the upper deck and l in the lower deck. The number...

A double-decker bus carry (u +l) passengers, u in the upper deck 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 (£ l) particular passengers refuse to go in the upper deck and s (£ u) refuse to sit in the lower deck , is/are

A

u–sCl–r

B

(u+l−r−s)!(l−r)!(u−s)!\frac{(u + \mathcal{l -}r - s)!}{(\mathcal{l -}r)!(u - s)!}

C

u–sPl – r

D

(u+l)!r!s!\frac{(u + \mathcal{l})!}{r!s!}

Answer

(u+l−r−s)!(l−r)!(u−s)!\frac{(u + \mathcal{l -}r - s)!}{(\mathcal{l -}r)!(u - s)!}

Explanation

Solution

No. of passengers to be allotted in the two decks bus

= (u + l) – (r + s)

Number of seats available in the upper deck

= (u –s)

\ Total no. of ways = (u+l−r−s)!(l−r)!(u−s)!\frac{(u + \mathcal{l -}r - s)!}{(\mathcal{l -}r)!(u - s)!}