An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the 2 people? Exercises \( 51-55 \). use counting principles to find the probability. Then tell

To determine how many ways an employer can hire 2 people from a list of 13 applicants, we can use the combination formula, which is given by: \[ C(n, r) = \frac{n!}{r!(n - r)!} \] where: - \( n \) is the total number of applicants, - \( r \) is the number of applicants to be chosen, - \( ! \) denotes factorial, which is the product of all positive integers up to that number. In this case, \( n = 13 \) and \( r = 2 \). Plugging in these values, we get: \[ C(13, 2) = \frac{13!}{2!(13 - 2)!} = \frac{13!}{2! \cdot 11!} \] Now, we can simplify this: \[ C(13, 2) = \frac{13 \times 12 \times 11!}{2! \times 11!} = \frac{13 \times 12}{2!} \] Calculating \( 2! \): \[ 2! = 2 \times 1 = 2 \] Now substituting back: \[ C(13, 2) = \frac{13 \times 12}{2} = \frac{156}{2} = 78 \] Thus, the employer can choose to hire 2 people from a list of 13 applicants in **78 different ways**. If you have specific exercises (51-55) that you would like to analyze for probability using counting principles, please provide those details, and I can assist you further!