If there are seven children lining up for recess, how many different ways can they line up?
what is 7! ?
To find the number of different ways the seven children can line up for recess, we can use the concept of permutations. In a permutation, the order matters.
The first child in line can be any one of the seven children. Once the first child is chosen, the second child can be any one of the remaining six children. Similarly, the third child can be any one of the remaining five children, and so on.
To determine the total number of permutations, we multiply the number of choices for each position together. For this particular scenario, we have 7 choices for the first child, 6 choices for the second child, 5 choices for the third child, and so on, until we have 1 choice for the seventh child.
Therefore, the total number of different ways the seven children can line up for recess is given by:
7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
So, there are 5040 different ways the seven children can line up.