Chapter 13.9, Problem 7PPS

To determine

To calculate: No. of ways that can the first three moves of the game occur.

Answer to Problem 7PPS

There are $504$ different ways that the players can take the first $3$ moves of the game.

Explanation of Solution

Given information:

No of moves in a game $=3$ .

Calculation:

In the game of tic toc toe there are total $9$ moves.

A permutation is an arrangement or listings in which the order is important, whereas selecting the first $3$ moves of the game, order is important.

Thus, use permutation.

As there are total $9$ number of moves, so there are total $9$ choices are available for the first move.

  $8$ choices are available for the second move.

  $7$ choices are available for the third move.

So, the number of different ways that the first $3$ moves of the game occur is as below:

  $\begin{array}{l}P\left(9,3\right)=9\times 8\times 7\\ =504\end{array}$