Chapter 13.2, Problem 7CFU

To determine

To find: Whether the arrangement of the objects is the linear or circular permutation and determine the number of arrangements for each situation.

Answer to Problem 7CFU

The required combination is $3628800$ and the condition iscircular permutation as the huddle is in the form of the circular and there is no reference point.

Explanation of Solution

Given:

The given condition is the 11 football players in the huddle.

Calculation:

The condition for the 11 football players in the huddle is the circular permutation as the huddle is in the form of the circular and there is no reference point.

Consider the number of permutation of $n$ things take all the time is,

  $\left(n-1\right)!$

Then, by the above concept the number of different ways of arranging the 11 football players is,

  $\begin{array}{c}\left(11-1\right)!=10!\\ =3628800\end{array}$