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JEE Main 202628 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
28 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2026 · 28 January · Evening Shift · Mathematics · Permutation and Combination

Three persons enter in a lift at the ground floor. The lift will go...

Three persons enter in a lift at the ground floor. The lift will go upto 10th 10^{\text{th }} floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ____\_\_\_\_.

Correct answer

0

Step-by-step solution

Three persons must exit at three different floors.
The lift goes to the 10th floor and does not stop at floors 1, 2, and 3.
Available floors for exit: 4, 5, 6, 7, 8, 9, 10 (7 floors total).
The number of ways to assign 3 persons to 3 different floors from 7 available floors is a permutation problem: P(7,3)=7×6×5=210P(7, 3) = 7 \times 6 \times 5 = 210.
Alternatively, choose 3 floors from 7 and arrange 3 persons: 7P3=35×6=210{}^{7}P_{3} = 35 \times 6 = 210.
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