Math Help - joint probability question

1. joint probability question

Hi!Can someone please help me with these 2 questions?
Thanks in advance!

1) The number of people entering the drugstore in a given hour is a Poisson random variable with parameter 10. Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour. What assumptions have you made?

2) Let
f(x,y) = 24xy 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ x+y ≤ 1
0 otherwise
Show that f(x,y) is a joint probability density function and find E(X).

2. What problems have you had so far? Please show some of your work!

3. we need more info on men vs women

$\int_0^1\int_0^{1-x}24xy dydx$ equals......

and

$E(X)=\int_0^1\int_0^{1-x}24x^2y dydx$