Question

What are the number of ways of arranging 9 books out of 14 in a library?

Answer 1

Given:

Number of books we should arrange = 9

Total number of books = 14

To find:

We need to find the number of ways of arranging the 9 books out of 14 in the library.

Solution:

According to the question, we should arrange 9 books out of 14.

Here, order of book is important. So, we use permutations to find the number of ways.

So, the number of ways $=\ {^{14}} P_9$

Now, we should find the value of ${^{14}} P_9$.

We know that, $^nP_r=\frac{n!}{(n-r)!}$.

Applying the above formula,

$\Rightarrow{^{14}} P_9$

$\Rightarrow \frac{14!}{(14-9)!}$

Simplifying the expression,

$\Rightarrow \frac{14!}{(5)!}$

$\Rightarrow \frac{14!}{5!}$

Therefore, the number of ways of arranging the books are $\frac{14!}{5!}$.