Chapter 11, Problem 14CT

To determine

To evaluate the given combination

Answer to Problem 14CT

The given combination is evaluated as,

  ${}_6{C}_6=1$

Explanation of Solution

Given information:the combination is given as,

  ${}_6{C}_6$

Calculation: the given combination can be evaluated as,

  $\begin{array}{l}{}_6{C}_6=\frac{{}_6{P}_6}{6!}\left[\text{use formula of combination }\right]\\ {}_6{C}_6=\frac{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}\left[{\text{write }}_6{P}_6\text{ and 6! as products}\right]\\ {}_6{C}_6=1\left[\text{divide out common factor}\right]\end{array}$

Therefore,

The given combination is evaluated as,

  ${}_6{C}_6=1$