Question

When the science group containing six children leaves the main class once a week for special instruction, the science teacher lines up the students and leads them to the science room. How many differenct ways can the teacher line up the six children?

Answer 1

for the step it is 6!=720
explanations:

assume there is 6 place for the student
_ _ _ _ _ _

There is 6 choice to put 1student
6 _ _ _ _ _
and there left 5 place and 5 students

for 2nd place it has 5 ways/choice

so after putting all students it will be:
6 5 4 3 2 1
so number of way u can line up the children is
6x5x4x3x2x1=6!=720