Chapter 11, Problem 4CST

To determine

To find the equivalent expression.

Answer to Problem 4CST

The expression which is equivalent to ${}_{20}{p}_{14}$ is $\frac{20!}{6!}$ . Thus option H. is the equivalent expression.

Explanation of Solution

Given information:

The expressions are given in the question as,

  $\frac{14!}{20!},\frac{6}{20!},\frac{20!}{6!}\text{ and }\frac{20!}{14!}$

From the given permutation,

  ${}_{20}{p}_{14}$

Here, $n=20\text{ and }r=14$

  $\begin{array}{l}{}_{20}{p}_{14}=\frac{20!}{\left(20-14\right)!}\\ {}_{20}{p}_{14}=\frac{20!}{6!}\end{array}$

From the above derivation, it can be concluded,

  ${}_{20}{p}_{14}=\frac{20!}{6!}$

Therefore,The expression which is equivalent to ${}_{20}{p}_{14}$ is $\frac{20!}{6!}$ . Thus option H. is the equivalent expression.