Chapter 0.5, Problem 6E

To determine

To evaluate: the given permutation.

Answer to Problem 6E

  $C{}_4=210$ .

Explanation of Solution

Given information:

  $C{}_4$

Solving the given permutation,

  $\begin{array}{c}C{}_4=\frac{10!}{4!\left(10-4\right)!}\\ =\frac{10!}{4!6!}\\ =\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 6\times 5\times 4\times 3\times 2\times 1}\\ =\frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}\\ =210\end{array}$

So,

After evaluating,

  $C{}_4=210$ .