Questions: Evaluate the expression. C(13,0)

Solution Steps

To evaluate the expression \( C(13,0) \), we need to use the combination formula, which is given by \( C(n, k) = \frac{n!}{k!(n-k)!} \). Here, \( n = 13 \) and \( k = 0 \).

1. Identify the values of \( n \) and \( k \).
2. Use the combination formula to calculate \( C(13,0) \).

To evaluate \( C(13,0) \), we use the combination formula: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] where \( n = 13 \) and \( k = 0 \).

Substituting the values into the formula gives: \[ C(13, 0) = \frac{13!}{0!(13-0)!} = \frac{13!}{0! \cdot 13!} \]

Since \( 0! = 1 \) and \( 13! \) cancels out, we have: \[ C(13, 0) = \frac{13!}{1 \cdot 13!} = 1 \]

Final Answer