In how many ways can a person select 3 golf shirts for vacation from a selection of 10 golf shirts?

To find the number of ways a person can select 3 golf shirts from a selection of 10 golf shirts, we can use the combination formula. The combination formula is given by: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] Where: - \( n \) is the total number of items to choose from (in this case, 10 golf shirts) - \( k \) is the number of items to choose (in this case, 3 golf shirts) - \( n! \) represents the factorial of \( n \), which is the product of all positive integers up to \( n \) Substitute the values into the formula: \[ C(10, 3) = \frac{10!}{3!(10-3)!} \] Now, we can calculate the number of ways to select 3 golf shirts from 10 golf shirts. Simplify the expression by following steps: - step0: Solution: \(\frac{10!}{\left(3!\times \left(10-3\right)!\right)}\) - step1: Remove the parentheses: \(\frac{10!}{3!\times \left(10-3\right)!}\) - step2: Subtract the numbers: \(\frac{10!}{3!\times 7!}\) - step3: Expand the expression: \(\frac{10\times 9\times 8\times 7!}{3!\times 7!}\) - step4: Simplify: \(\frac{10\times 9\times 8}{3!}\) - step5: Multiply: \(\frac{720}{3!}\) - step6: Calculate the value: \(\frac{720}{6}\) - step7: Reduce the fraction: \(120\) The number of ways a person can select 3 golf shirts from a selection of 10 golf shirts is 120 ways.