Mathematics · Permutations and Combinations

JEE Main 2026 — 28 January, Evening Shift — Question 22

Three persons enter in a lift at the ground floor. The lift will go upto $10^{\text {th }}$ 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 $\_\_\_\_$

Answer: 210

Numerical answer — enter this value.

Step-by-step solution

The lift does not stop at floors 1, 2, and 3, so available floors are 4 to 10, i.e., 7 floors. Choose 3 distinct floors out of 7: $\binom{7}{3}$ ways. The 3 persons can exit at these 3 floors in $3!$ ways. Total number of ways = $\binom{7}{3} \times 3! = 35 \times 6 = 210$ .

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 28 January, Evening Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Applications of Permuations and Combination