Use the formula for \( { }_{n} C_{r} \) to evaluate the given expression. \( \frac{{ }_{8} C_{5}}{{ }_{4} C_{3}} \) \( \frac{{ }_{8} C_{5}}{{ }_{4} C_{3}}=\square \) (Type an integer or a simplified fraction.)

To solve \( \frac{{ }_{8} C_{5}}{{ }_{4} C_{3}} \), we start by using the formula for combinations, which is given by: \[ { }_{n} C_{r} = \frac{n!}{r!(n-r)!} \] Calculating \( { }_{8} C_{5} \): \[ { }_{8} C_{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56 \] Now, calculating \( { }_{4} C_{3} \): \[ { }_{4} C_{3} = \frac{4!}{3!(4-3)!} = \frac{4!}{3! \cdot 1!} = \frac{4}{1} = 4 \] Now, putting it all together: \[ \frac{{ }_{8} C_{5}}{{ }_{4} C_{3}} = \frac{56}{4} = 14 \] Thus, \( \frac{{ }_{8} C_{5}}{{ }_{4} C_{3}} = 14 \).