Questions: Calculate the indicated quantity. C(7,5)

Solution Steps

To calculate \( C(7,5) \), we need to use the combination formula \( C(n, k) = \frac{n!}{k!(n-k)!} \). Here, \( n = 7 \) and \( k = 5 \). We will use Python's math library to compute the factorials and then apply the combination formula.

To calculate the combination \( C(7,5) \), we use the formula: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] where \( n = 7 \) and \( k = 5 \).

Calculate the factorials of \( n \), \( k \), and \( n-k \): \[ 7! = 5040 \] \[ 5! = 120 \] \[ (7-5)! = 2! = 2 \]

Substitute the factorial values into the combination formula: \[ C(7, 5) = \frac{5040}{120 \times 2} \] \[ C(7, 5) = \frac{5040}{240} \] \[ C(7, 5) = 21 \]

Final Answer