\frac{{8\choose 3}\cdot {6\choose 4}}{{14\choose 7}}=
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S - the set of all equally likely outcomes
n(S) - total number of outcomes in S
A - the event
n(A) - total number of outcomes in A
The probability of A happening given by formula
P(A)=\frac{n(A)}{n(S)}
n(S)={14\choose 7}=\frac{14!}{7!\cdot 7!}=3432
n(A)={8\choose 3}\cdot {6\choose 4}=\frac{8!}{5!\cdot 3!}\cdot \frac{4!}{2!\cdot 4!}=56\cdot 15=840
P(A)=\frac{840}{3432}=\frac{35}{143}