Chapter 13.1, Problem 13CFU

To determine

To calculate: The number of different ways to arrange 10 students in a row.

Answer to Problem 13CFU

The number of different ways to arrange10 students in a roware $3628800$ .

Explanation of Solution

Given information:

The number of students in a group are 10.

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 students in a group are 10.

To arrange 10 students in a row, there are 10 ways to make sit a student at first place then 9 ways toarrange at second place, 8 ways to arrange at third place and so on.

Therefore, number of ways are $P\left(10,10\right)$

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 10.

  $\begin{array}{c}P\left(10,10\right)=10!\\ =10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\\ =3628800\end{array}$

Thus, the number of different ways to arrange 10 students in a row are $3628800$ .