How many different permutations can be created when anne, Becky,Carlo, dan and Esi line up to buy movie tickets, if Esi always stand behind becky?

Answer 1

If Esi is always behind Becky, we have only 4 independent choices for each position.
So for the first position, there are 4 choices, for the second, 3 choices left, then 2, then 1.
The number of permutations is the product of the 4 numbers.