Chapter 12, Problem 121CUR

To determine

To evaluate: ${}_{16}{c}_{10}$

Answer to Problem 121CUR

The simplified answer is 8008.

Explanation of Solution

Given information:

The given information is, ${}_{16}{c}_{10}$

Formula used:

Formula of permutation is used.

  ${}_n{c}_r=\frac{{}_n{p}_r}{r!}$

Calculation:

  $\begin{array}{l}To\text{ evaluate the equation;}\\ {}_n{c}_r=\frac{{}_n{p}_r}{r!}\\ {}_{16}{c}_{10}=\frac{{}_{16}{c}_{10}}{10!}\\ {}_{16}{c}_{10}=\frac{16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\ {}_{16}{c}_{10}=8008.\end{array}$