Question

Passengers are to travel by a double decker bus which can accomodate $13$ 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?

• A. $25$
• B. $21$
• C. $18$
• D. $15$

Answer 1

The correct option is B $21$

As $5$ refuse to sit in the upper deck so they must sit in lower deck, similarly $8$ refused to sit in the lower deck so they must sit in upper deck.

That means $5+8=13$ person are alloted the sits.

Now remaining $7$ can sit in lower as well as upper deck.

Two sits are available in lower deck$(\because 5$ are already allotted out of $7.)$

Number of ways to choose $2$ out of $7={{}^{7}C}_2$.

Remaining $5$ must sit in upper deck. So total ways$={{}^{7}C}_2.=21$

Hence, $\left(B\right)$