Three persons enter in a lift at the ground floor. The lift will go up to 10th floor

Q. Three persons enter in a lift at the ground floor.

The lift will go up to 10th 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: 210

Explanation

The lift does not stop at the first, second and third floors.

So the possible floors where a person can exit are:

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

Total available floors = 7

Three persons must exit at three different floors.

The number of ways of choosing 3 different floors out of 7 is:

${}^7C_3 = 35$

The three persons are distinct, so they can exit in:

$3! = 6$ ways

Hence, total number of ways:

$35 \times 6 = 210$

Therefore, the required number of ways is:

$210$

Related JEE Main Questions

If ∑ from r = 1 to 25 ( r / (r⁴ + r² + 1) ) = p/q, where p and q are positive integers such that gcd(p, q) = 1, then p + q is equal to ______.

The sum of the coefficients of x^499 and x^500 in (1 + x)^1000 + x(1 + x)^999 + x^2(1 + x)^998 is :

The sum of all the elements in the range of f(x) = Sgn(sin x) + Sgn(cos x) + Sgn(tan x) + Sgn(cot x), x ≠ nπ/2, n ∈ Z, where Sgn(t) = { 1, if t > 0; −1, if t < 0 } is :

Let P1 : y = 4x^2 and P2 : y = x^2 + 27 be two parabolas. If the area of the bounded region enclosed between P1 and P2 is six times the area of the bounded region enclosed between the line y = αx, α > 0 and P1, then α is equal to :

Let the ellipse E : x^2/144 + y^2/169 = 1 and the hyperbola H : x^2/16 − y^2/λ^2 = −1 have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of 24(e + L) is :

JEE Main Chapter-wise Previous Year Questions