Chapter 13.2, Problem 27E

To determine

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

Answer to Problem 27E

The number of different ways of arranging the $10$ different beads on a string is $3,628,800$ .

Explanation of Solution

Given information: $10$ different beads on a string.

The number of linear permutations of $n$ things taken all at a same time as $n!$ .

Since the given string is linear hence the arrangement is li near permutation and the number of different ways of arranging the $10$ different beads on string is given by using the formula $n!$ .

Here, $n=10$ .

Substitute $10$ for $n$ in $n!$ .

  $\begin{array}{c}10!=9!\\ =9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\\ =3,628,800\end{array}$

Therefore, the number of different ways of arranging the $10$ different beads on a string is $3,628,800$ .