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A double-decker bus has 5 empty seats upstairs and 5 empty seats downstairs. 10 people aboard the bus of which 2 are old people and 3 are children. The children refuse to take seats down stairs while old people insist on staying down stairs. In how many different arrangements can the 10 people take seats in the bus.

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144000

72000

36000

18000

answer is A.

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Detailed Solution

Total No. of ways = No. of ways to assign 2 seat down to old +No. of ways to assign 3 seats to children +No. of ways of arranging the remaining 5 people
=

C_{3}^{5} \times

3!×

C_{3}^{5}

×2!.5! =144000

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