In how many ways can you select a 9 member committee from a pool of 20 candidates?

To find the number of ways to select a 9-member committee from a pool of 20 candidates, 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 candidates (20 in this case) - \( k \) is the number of members to be selected (9 in this case) - \( n! \) represents the factorial of \( n \), which is the product of all positive integers up to \( n \) Substitute the values into the formula: \[ C(20, 9) = \frac{20!}{9!(20-9)!} \] Now, we can calculate the number of ways to select a 9-member committee from a pool of 20 candidates. Simplify the expression by following steps: - step0: Solution: \(\frac{20!}{\left(9!\times \left(20-9\right)!\right)}\) - step1: Remove the parentheses: \(\frac{20!}{9!\times \left(20-9\right)!}\) - step2: Subtract the numbers: \(\frac{20!}{9!\times 11!}\) - step3: Multiply the terms: \(\frac{20!}{14485008384000}\) - step4: Calculate the value: \(\frac{2432902008176640000}{14485008384000}\) - step5: Reduce the fraction: \(167960\) There are 167,960 ways to select a 9-member committee from a pool of 20 candidates.