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DIY Challenge 2: Arranging four balls

If we had 3 balls, we see that we can arrange them in 6 different ways.

We want to find the total ways to arrange if there were 4 balls. One way could be to write down or draw all the possible ways.

Can you think of an easier way to count the total number of ways to arrange 4 balls?

What students worked out11

  • Student 11

    First we will take any ball of any colour
    Make all the combinations of the ball which are left. Similarly take one more ball and make the combinations.like this do that with all the balls.

  • Student 11

    Take any ball of any colour then make as much as combinations you can make,for three ball there are 6 as Sir has said. Similarly do this with all the balls

  • Student 1

    You fix a colour at the start and one after the first one and change the last two then change the one next to the first fixed one do it with all 3 colours the make the staring one different and fix the one next to it and so on…

    • Student 1

      I got 24 ways as my total

  • Student 9

    We have six different ways to arrange three balls uniquely. When I add a fourth ball, the new ball can go in four different positions in the sequence of three balls. This means I have 4 x 6 OR 24 ways of arranging four balls.

  • Student 4

    We have 6 ways of arranging 3 balls. So if we add a fourth ball, we will be able to place it in all four positions for all colors at the beginning. So we will have to multiply 6×4 to get the total of 24 rearrangement possibilities

  • Student 2

    there are 24 ways total
    EASIEST METHOD:-
    PUT ANY BALL FIRST eg: GREEN(g)
    we can arrange the rest 3 in 6 ways
    so we get six ways with each ball first
    6×4
    =24
    🙂

  • Student 15

    the formula of finding the total of next ball is the Number of ways for the predecessor of the no. of balls X Number of balls. So to find for four balls quickly we need to multiply 4 X 6

  • Student 14

    To find the ways of three balls, we make one group,
    to find all the ways of four balls,
    we make two groups of balls, each with 3 balls.
    As three balls have 6 ways and there are two groups
    each with six ways, we multiply the ways and we get
    36 ways.

  • Student 3

    24 ways
    6 ways each by keeping one color ball first
    so 6×4 ways

  • Student 17

    6 ways to arrange the balls starting with the 1st then 2nd then 3rd then 4rth color, so 6 ways taken the 4 balls = 24