Step 1 :First, we need to calculate the combinations separately. The formula for combination is \(\frac{n!}{r!(n-r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to choose.
Step 2 :Calculate the first combination \(\left(\begin{array}{l}3 \\ 1\end{array}\right)\), which equals to 3.
Step 3 :Calculate the second combination \(\left(\begin{array}{c}10-3 \\ 5-1\end{array}\right)\), which equals to 35.
Step 4 :Calculate the third combination \(\left(\begin{array}{c}10 \\ 5\end{array}\right)\), which equals to 252.
Step 5 :Substitute these values into the original equation: \(\frac{3 \times 35}{252}\), which simplifies to approximately 0.4166666666666667.
Step 6 :Final Answer: \(\boxed{0.4166666666666667}\)