Evaluate the expression. \[ { }_{12} \mathrm{C}_{5} \] \[ { }_{12} C_{5}= \]

Step 1 ：The given expression is a combination, which is a way of selecting items without considering the order. In mathematics, a combination is represented as nCr where n is the total number of items, and r is the number of items to select.

Step 2 ：The formula to calculate a combination is: \(nCr = \frac{n!}{r!(n-r)!}\) where '!' denotes factorial, which is the product of all positive integers up to that number.

Step 3 ：In this case, n is 12 and r is 5. So, we need to calculate the factorial of 12, 5, and (12-5), and then substitute these values into the formula.

Step 4 ：Calculate the factorial of n (12): \(12! = 479001600\)

Step 5 ：Calculate the factorial of r (5): \(5! = 120\)

Step 6 ：Calculate the factorial of (n-r) (12-5): \((12-5)! = 5040\)

Step 7 ：Substitute these values into the formula: \(\frac{479001600}{120 \times 5040} = 792.0\)

Step 8 ：Final Answer: The value of the expression \({ }_{12} \mathrm{C}_{5}\) is \(\boxed{792}\)