Questions: Use the formula for nCr to evaluate the given expression. 16C1= (Type an integer or a simplified fraction.)

Solution Steps

To solve for \({ }_{16} C_{1}\), we use the combination formula \({ }_{n} C_{r} = \frac{n!}{r!(n-r)!}\). Here, \(n = 16\) and \(r = 1\). Plugging these values into the formula will give us the result.

To evaluate \({ }_{16} C_{1}\), we use the combination formula: \[ { }_{n} C_{r} = \frac{n!}{r!(n-r)!} \] Substituting \(n = 16\) and \(r = 1\): \[ { }_{16} C_{1} = \frac{16!}{1!(16-1)!} = \frac{16!}{1! \cdot 15!} \]

We can simplify the expression: \[ { }_{16} C_{1} = \frac{16 \times 15!}{1 \times 15!} = \frac{16}{1} = 16 \]

Final Answer