Question

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 can be divided 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 $21$

$\because 5$ have refused for upper deck

$\therefore$ they will be in lower deck $8$ will be in upper deck

Remaining persons $=7$

Seat remaining in upper deck $=5$

No. of ways $={}^7{C}_5$

And person remaining $=2$ and seats are $2\therefore$ no. of ways $={}^2{C}_2$

$\therefore$ Total ways $={}^7{C}_5\times {}^2{C}_2$

$=21$

Hence the answer is $21.$