Probability that minimum of two numbers is less than 4 Suppose I have to choose two numbers from set $$S=\{1,2,3,4,5,6 \}$$ without a replacement , then what is the probability that minimum of two is less than $4$?
I made two groups for this problem $A= \{1,2,3 \}$ and $B=\{4,5,6 \}$
.There are two possibilities , either both are from $A$ or one from $A$ and one from $B$ to satisfy our requirement. Hence
$$P(E)=\frac{3}{6}.\frac{2}{5} + \frac{3}{6}.\frac{3}{5}$$
but answer is incorrect. Help?

We have $\binom{6}{2}$ possibilities, but $\binom{3}{2}$ of them are not what we want, more precisely, those events that 2 elements are chosen from $\{4,5,6\}$, hence, $P(E)=\frac{\binom{6}{2}-\binom{3}{2}}{\binom{6}{2}}$.
