JEE Main · 2026 · 28 Jan 2026 · Shift 2 · Permutations and Combinations

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

1 0^{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

Solution

The lift does not stop at floors

1, 2, 3

, so the usable floors are

4, 5, 6, 7, 8, 9, 10

— seven in all. Each of the three persons leaves at a different floor, so the count is the number of ordered selections of

3

floors from

7

^{7} P_{3} = 7 \times 6 \times 5 = 210.

The three persons can exit at three different floors in

210

ways.

JEE Main · 2026 · 28 Jan 2026 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Permutations and Combinations →

More JEE Main questions on Permutations and Combinations

The number of strictly increasing functions f from the set ${1, 2, 3, 4, 5, 6}$ to the set $(1, 2, 3, \dots, 9)$ such that $f (i) \neq = i$ for $1 \leq i \leq 6$ , is equal to :
JEE Main 2026View solution →
Let $S = {(m, n) : m, n \in {1, 2, 3, \dots .., 50}}$ . If the number of elements ( $m, n$ ) in S such that $6^{m} + 9^{n}$ is a multiple of 5 is p and the number of elements …
JEE Main 2026View solution →
The largest $n \in N$ , for which $7^{n}$ divides 101!, is:
JEE Main 2026View solution →
Let ABC be a triangle. Consider four points $p_{1}, p_{2}$ , $p_{3}, p_{4}$ on the side AB , five points $p_{5}, p_{6}, p_{7}, p_{8}, p_{9}$ on the side BC and four points …
JEE Main 2026View solution →
Let S be the set of the first 11 natural numbers. Then the number of elements in $A = {B \subseteq S : n (B) \geq 2$ and the product of all elements of B is even $}$ is
JEE Main 2026View solution →
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.
JEE Main 2026View solution →