Use a calculator to evaluate \( { }_{27} \mathrm{C}_{12} \). \( { }_{27} \mathrm{C}_{12}=\square \) (Simplify your answer. Type an integer or a fraction.)

To evaluate \( { }_{27} \mathrm{C}_{12} \), we use the formula for combinations: \[ { }_{n} \mathrm{C}_{r} = \frac{n!}{r!(n-r)!} \] In this case, \( n = 27 \) and \( r = 12 \): \[ { }_{27} \mathrm{C}_{12} = \frac{27!}{12!(27-12)!} = \frac{27!}{12! \times 15!} \] Calculating this gives: \[ { }_{27} \mathrm{C}_{12} = \frac{27 \times 26 \times 25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 \times 17 \times 16}{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \] Evaluating the numerator and the denominator, we find: \[ { }_{27} \mathrm{C}_{12} = 17383860 \] So, the value of \( { }_{27} \mathrm{C}_{12} \) is \( 17383860 \).