Evaluate the expression.
a) ${ }_{8} \mathrm{C}_{3}$
b) ${ }_{8} \mathrm{P}_{3}$
a) ${ }_{8} C_{3}=56$ (Simplify your answer.)
b) ${ }_{8} \mathrm{P}_{3}=\square$ (Simplify your answer.)

Step 1 ：The problem is asking to evaluate the combination and permutation expressions. The combination expression \({ }_{8} C_{3}\) is asking for the number of ways to choose 3 items from a set of 8, without regard to order. The permutation expression \({ }_{8} P_{3}\) is asking for the number of ways to arrange 3 items from a set of 8, where order does matter.

Step 2 ：To calculate these, we can use the formulas for combinations and permutations. The formula for combinations is \({ }_{n} C_{r} = \frac{n!}{r!(n-r)!}\), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial. The formula for permutations is \({ }_{n} P_{r} = \frac{n!}{(n-r)!}\).

Step 3 ：For the first question, we have already calculated the combination expression \({ }_{8} C_{3}\) to be 56.

Step 4 ：For the second question, we need to calculate the permutation expression \({ }_{8} P_{3}\).

Step 5 ：Let's substitute n = 8 and r = 3 into the permutation formula: \({ }_{8} P_{3} = \frac{8!}{(8-3)!}\).

Step 6 ：After calculating, we find that \({ }_{8} P_{3} = 336\). This is the number of ways to arrange 3 items from a set of 8, where order does matter.

Step 7 ：So, the final answer is \(\boxed{336}\).