% Birthday Problem
n=23;
1-(364/365)^{n-1}
i=(365-n+1):365;
1-prod(i./365)

n=60;
1-(364/365)^{n-1}
i=(365-60+1):365;
1-prod(i./365)

% State Lottery Problem
1-nchoosek(35,6)/nchoosek(40,6)