Nine stuffed characters, all different are placed along a baby’s toy shelf. How many possible arrangements are there if there are no restrictions.
To find the number of possible arrangements, we can use the concept of permutations.
Since there are nine different stuffed characters, we have nine choices for the first position on the toy shelf. Once that character is placed, we have eight choices for the second position, then seven choices for the third position, and so on, until we have only one choice for the ninth position.
Therefore, the total number of possible arrangements is given by:
9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
So, there are 362,880 possible arrangements if there are no restrictions.
To find the number of possible arrangements of the nine stuffed characters without any restrictions, we can use the concept of permutations.
In a permutation, the order of the objects matters. Since all the stuffed characters are different, we need to consider their specific positions on the toy shelf.
The formula to calculate the number of permutations is given by:
n! (n factorial) = n x (n-1) x (n-2) x ... x 3 x 2 x 1,
where n represents the number of objects.
In this case, n = 9, as there are nine stuffed characters.
Therefore, the number of possible arrangements is:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880.
So, there are 362,880 possible arrangements if there are no restrictions.