Evaluate \( { }^{8} C_{4} \)

To evaluate \( { }^{8} C_{4} \), we use the formula for combinations: \[ { }^{n} C_{r} = \frac{n!}{r!(n-r)!} \] In this case, \( n = 8 \) and \( r = 4 \). Plugging these values into the formula gives: \[ { }^{8} C_{4} = \frac{8!}{4!(8-4)!} = \frac{8!}{4! \cdot 4!} \] Calculating the factorials, we find: \[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320, \] \[ 4! = 4 \times 3 \times 2 \times 1 = 24, \] \[ (8-4)! = 4! = 24. \] Substituting these back into our formula yields: \[ { }^{8} C_{4} = \frac{40320}{24 \times 24} = \frac{40320}{576} = 70. \] Thus, the value of \( { }^{8} C_{4} \) is \( \boxed{70} \).