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A double-decker bus has 5 empty seats in the upstair and 5 emp

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?

144000

72000

36000

18000

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Alexander Discussed

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?

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Text solutionVerified

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

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Question Text	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?
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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