In a train,there are 5 vacant seats. In how m | vedclass

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(D) To find the number of ways $3$ passengers can sit in $5$ vacant seats,we use the concept of permutations because the order in which they sit matte

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$60$

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(D) To find the number of ways $3$ passengers can sit in $5$ vacant seats,we use the concept of permutations because the order in which they sit matters.The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 5$ (total seats) and $r = 3$ (passengers).Therefore,the number of ways is $^5P_3 = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 	imes 4 	imes 3 	imes 2 	imes 1}{2 	imes 1} = 5 	imes 4 	imes 3 = 60$.Thus,there are $60$ ways for the passengers to sit.

In a train,there are $5$ vacant seats. In how many ways can $3$ passengers sit on these seats?

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