Chapter 13.1, Problem 44E

To determine

To calculate: The number of different ways to display 11 paintings on a wall.

Answer to Problem 44E

The number of different ways to display 11 paintings on a wallare $39916800$ .

Explanation of Solution

Given information:

The number of paintings to be displayed on wall are 11.

Formula used:

If there are n objects taken n at a time then permutation is defined as $P\left(n,n\right)=n!$ .

Calculation:

Consider the provided information that number of paintings to be displayed on wall are 11.

To display 11 paintings, there are 11 ways to display the painting at first place then 10 ways to display at second place, 9 ways to display a painting a t third place and so on.

Therefore, number of ways are $P\left(11,11\right)$

Recall that if there are n objects taken n at a time then permutation is defined as $P\left(n,n\right)=n!$ .

Here n is 11.

  $\begin{array}{c}P\left(11,11\right)=11!\\ =11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\\ =39916800\end{array}$

Thus, the number of different ways to display 11 paintings on a wall are $39916800$ .