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

1) 25

2) 21

3) 18

4) 15

Answer: (2) 21

Solution: 13 can be accommodated in upper deck and 7 in the lower deck

5 passengers refused to sit in upper deck

We have 7 seats in lower deck that can be taken by 5 passengers in 7C5 ways

Now, there are 2 passengers and 2 seats left, so they can be seated in 2C2 ways

Therefore, total number of ways = 7C5 x 2C2 = 21

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