# P(range(a,b)) is probability of standard normal distribution in range(a,b); 
# P(n,k):=n!/(n-k)! permutation;

P(x_<b_):=Phi(left(solve(x-b,x)));
P(x_<=b_):=Phi(left(solve(x-b,x)));
P(x_>a_):= 1-Phi(left(solve(x-a,x)));
P(x_>=a_):= 1-Phi(left(solve(x-a,x)));

P(a_<x_<b_):=Phi(solve(x-b,x))-Phi(solve(x-a,x));
P(a_<=x_<=b_):=Phi(solve(x-b,x))-Phi(solve(x-a,x));
P(b_>x_>a_):=Phi(solve(x-b,x))-Phi(solve(x-a,x));
P(range(a_,b_)):=Phi(b)-Phi(a);

P(n_,k_):=n!/(n-k)!;