If X is a binomial random variable with expected value 6 & variance 2.4, find P(X=5).

Question:

If X is a binomial random variable with expected value 6 and variance 2.4, find P(X=5).

My try:

I know this question is simple, but I think I'm making a silly mistake in my logic somehow. I started with E(x)=np and Var(X)=E(X^2) - (E(X))^2 so Var(X)= npq - (np)^2. I plugged in all the numbers, solved, and got q=6.4 ... yeah way off, q has to be between 0 and 1. So I stopped there since my implementation was obviously wrong.

Thanks for any and all help.