(D) The building has $12$ floors. Since the persons enter the lift, they must leave at floors other than the ground floor (where they entered). This l

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(D) The building has $12$ floors. Since the persons enter the lift, they must leave at floors other than the ground floor (where they entered). This leaves $12 - 1 = 11$ possible floors. However, the lift does not stop at the second floor, so the number of available floors for them to exit is $11 - 1 = 10$. Since the $3$ persons leave at different floors, the number of ways is given by the permutation of $10$ floors taken $3$ at a time: $^{10}P_{3} = \frac{10!}{(10-3)!} = 10 \times 9 \times 8 = 720$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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In a $12$-storied building, $3$ persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

WBJEE 2020 All WBJEE

A
$36$
B
$120$
C
$240$
D
$720$

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Permutations and Combinations

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

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In a $12$-storied building, $3$ persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

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