Evaluate the following combination.
\[
{ }_{15} C_{3}
\]

Answer
\[
{ }_{15} C_{3}=
\]

Step 1 ：Given the combination expression \({ }_{15} C_{3}\).

Step 2 ：We will calculate this using the formula for combinations, which is \(\frac{n!}{r!(n-r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to choose.

Step 3 ：Substitute \(n = 15\) and \(r = 3\) into the formula, we get \(\frac{15!}{3!(15-3)!}\).

Step 4 ：Calculate the factorial of 15, 3, and 12 (which is 15 - 3).

Step 5 ：Substitute these values back into the formula, we get \(\frac{1307674368000}{6*479001600}\).

Step 6 ：Simplify the expression to get the final answer.

Step 7 ：Final Answer: \({ }_{15} C_{3} = \boxed{455}\)