Question

A double-decker bus has $5$ empty seats in the upstair and $5$ empty seats in the downstair. $10$ people board the bus of which, $2$ are old people and $3$ are children. The children refuse to take seats down stair while old people insist to stay down stair. In how many different arrangements can the $10$ people take seats in the bus?

• A. 144000
• B. 72000
• C. 36000
• D. 18000

Answer 1

Answer: (A)

144000

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 reamining 5 people
= ${}^5{C}_3.3!{\times }^5{C}_2\times 2!.5!$
=144000