Confusion in solving

Question

An apartment building has 11 residents. There are 7 residents on the second floor and 4 residents on the third floor. Six people use the elevator at random to go to their apartments. What is the probability that at most 3 of the residents exit on the second floor.?

I am solving as follows:

P(at most 3 will exit on 2nd floor) = P(0 will exit) + P( 1 will exit) + P( 2 will exit) + P( 3 will exit)

P(0 will exit) = 7C0 / 11C6
P(1 will exit) = 7C1 / 11C6
P(2 will exit) = 7C2 / 11C6
P(3 will exit) = 7C3 / 11C6

So when I sum up I am getting the answer as 64/442. Is it correct? And how can we use a random variable to solve this problem? Please help me. I am poor in probability.

Answer 1

Note that at most 4 will exit on the 3rd floor because there are 4 3rd-floor residents in total.