Permutation and Combination-1

   Now, there are four toy balls of red, yellow, blue and green, and assume the situation that a child is playing to arrange these four balls in a line. Let's think about how many ways he can line them up.

Fig. A-1 Four different colored balls; Red, Yellow, Blue and Green.

   In the playing with four balls, a child can arbitrary pick any of four colored balls up, and then place it on the first row. Therefore, a child have four ways for his first selection as shown in Fig. A-1.

Fig. A-2 Ways to place a ball in each trial.

   After the first choice, a child can also arbitrary pick one in the rested three balls up and place it on the second row, which means that a child has three choice to select a ball.
   If continuing this process to the last, a child will eventually be forced to chose the last remaining ball in the fourth trial.That is, 4 choices in the first trial; 3 choices in the second trial; 2 choices in the third trial; only 1 choice in the fourth trial.
   Then, it can be said that total possible ways to arrange four balls in a line are 24, which can be calculated from 4!=4x3x2x1 and called permutation.
   However, it should be noticed that all possible ways in the permutation are totally different arrangements, and therefore distinguishable as shown in Fig. A-3.

Fig. A-3 All possible 24 ways to line up four different colored balls.