Questions: Find the value of the combination. 7C6 7C6=

Solution Steps

To find the value of the combination \({ }_{7} \mathrm{C}_{6}\), we use the combination formula: \[ { }_{n} \mathrm{C}_{r} = \frac{n!}{r!(n-r)!} \] Here, \(n = 7\) and \(r = 6\). We will calculate the factorial of these numbers and then apply the formula.

To find the value of \({ }_{7} \mathrm{C}_{6}\), we use the combination formula: \[ { }_{n} \mathrm{C}_{r} = \frac{n!}{r!(n-r)!} \] where \(n = 7\) and \(r = 6\).

Substituting the values into the formula gives: \[ { }_{7} \mathrm{C}_{6} = \frac{7!}{6!(7-6)!} = \frac{7!}{6! \cdot 1!} \]

We can simplify this expression: \[ { }_{7} \mathrm{C}_{6} = \frac{7 \cdot 6!}{6! \cdot 1} = \frac{7}{1} = 7 \]

Final Answer