Question

A double decker bus can have (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 – s}C_{l – r}
• B. $\frac{(u\mathcal{+ l–}r–s)!}{\mathcal{(l–}r)!(u–s)!}$
• C. ^{u – s}P_{l – r}
• D. $\frac{(u + \mathcal{l})!}{r!s!}$

Answer 1

Answer: (B)

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

Answer 2

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