Nine stuffed characters, all different are placed along a baby’s toy shelf. How many possible arrangements are there if Cookie Monster must be in the middle
In this case, Cookie Monster must be in the middle of the shelf.
To solve this, we can consider the two sections of the shelf: left and right of Cookie Monster.
The left section can have 4 different characters (since Cookie Monster is already placed), and the right section can also have 4 different characters (since all characters are different).
Therefore, the total number of possible arrangements would be 4 choices for the left section × 1 choice for the middle (since Cookie Monster is fixed in the middle) × 4 choices for the right section.
Thus, there would be 4 × 1 × 4 = 16 possible arrangements.
To determine the number of possible arrangements with Cookie Monster in the middle, we can fix its position and calculate the number of arrangements for the remaining eight characters.
Since Cookie Monster must be in the middle, we can treat it as a reference point and divide the remaining eight characters into two groups of four on either side.
The number of ways to arrange four characters on one side of Cookie Monster is given by 4 factorial (4!), which is equal to 4 x 3 x 2 x 1 = 24.
Similarly, the number of ways to arrange the other four characters on the opposite side is also 4 factorial (4!).
Therefore, the total number of possible arrangements with Cookie Monster in the middle is given by:
Number of arrangements = Number of arrangements on one side x Number of arrangements on the other side
Number of arrangements = 4! x 4! = 24 x 24 = 576
So, there are 576 possible arrangements if Cookie Monster must be placed in the middle.