(D) The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 5$

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(D) The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 5$ (vacant seats) and $r = 3$ (passengers).Therefore,the number of ways is $^5P_3 = \frac{5!}{(5-3)!} = \frac{5 \times 4 \times 3 \times 2!}{2!} = 5 \times 4 \times 3 = 60$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In a train,five seats are vacant. In how many ways can three passengers sit?

A
$20$
B
$30$
C
$10$
D
$60$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In a train,five seats are vacant. In how many ways can three passengers sit?

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