Question

In how many ways can five children stand in a queue?

Answer 1

The number of ways that 5 children stand in a queue is 5!
5! = 5 * 4 * 3 * 2 * 1
    = 120 ways.

Answer 2

5 persons can occupy 5 positions - with out any restrictions. 

Assuming that it is a linear queue and not circular queue.

 Any of the 5 children can occupy the  1st position, any of the remaining 4 persons can occupy the second,  any of the remaining 3 persons can occupy the third position  and so on...

number of ways is  =  5 * 4 * 3 * 2 * 1  = 5 ! = 120