Use the formula for \( { }_{n} \mathrm{C}_{\mathrm{r}} \) to evaluate the given expression. \( { }_{22} \mathrm{C}_{4} \) \( { }_{22} \mathrm{C}_{4}=\square \) (Type an integer or a simplified fraction.)

To evaluate \( { }_{22} \mathrm{C}_{4} \), we can use the formula for combinations: \[ { }_{n} \mathrm{C}_{r} = \frac{n!}{r!(n-r)!} \] For \( n = 22 \) and \( r = 4 \): \[ { }_{22} \mathrm{C}_{4} = \frac{22!}{4!(22-4)!} = \frac{22!}{4! \cdot 18!} \] Now, we can simplify this: \[ { }_{22} \mathrm{C}_{4} = \frac{22 \times 21 \times 20 \times 19}{4 \times 3 \times 2 \times 1} \] Calculating the numerator: \[ 22 \times 21 = 462 \] \[ 462 \times 20 = 9240 \] \[ 9240 \times 19 = 175560 \] Now, calculating the denominator: \[ 4 \times 3 \times 2 \times 1 = 24 \] Finally, we divide the results: \[ { }_{22} \mathrm{C}_{4} = \frac{175560}{24} = 7315 \] So, \( { }_{22} \mathrm{C}_{4} = 7315 \).