In how many ways can a member of a hiring committee select 3 of 12 job applicants for further consideration?

The number of ways to select 3 job applicants out of 12 can be calculated using the combination formula. The combination formula is given by: \[ C(n, r) = \frac{n!}{r!(n-r)!} \] In this case, \( n = 12 \) (total number of job applicants) and \( r = 3 \) (number of job applicants to be selected). Substitute the values into the combination formula to find the number of ways to select 3 job applicants out of 12. Simplify the expression by following steps: - step0: Solution: \(\frac{12!}{\left(3!\times \left(12-3\right)!\right)}\) - step1: Remove the parentheses: \(\frac{12!}{3!\times \left(12-3\right)!}\) - step2: Subtract the numbers: \(\frac{12!}{3!\times 9!}\) - step3: Expand the expression: \(\frac{12\times 11\times 10\times 9!}{3!\times 9!}\) - step4: Simplify: \(\frac{12\times 11\times 10}{3!}\) - step5: Multiply: \(\frac{1320}{3!}\) - step6: Calculate the value: \(\frac{1320}{6}\) - step7: Reduce the fraction: \(220\)