Mathematics · Permutations and Combinations

JEE Main 2026 — 6 April, Evening Shift — Question 27

A building has ground floor and $10$ more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $10$ th floor. The number of ways, in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

Option A:
$2184$
Option B:
$3064$
Option C:
$7056$
Correct
Option D:
$11340$

Answer: C

Step-by-step solution

Form group of 4 and 5 person $\frac{9!}{4!5!}=126$ choose two floor out of 8 floor ${ }^{8} \mathrm{C}_{2}=28$ Total ways in which 4 & 5 persons can leave at different floor $126 \times 28 \times 2=7056$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 6 April, Evening Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Problems based on both permutations and combinations