Query about question "A fair coin with two sides, heads and tails,..." [40]

GRE GRE Quant Problem Solving
1

https://www.gregmat.com/problems/quant?problem=a-fair-coin-with-two-sides-heads-and-tails

I am having trouble understanding this. This says 5 heads and 5 tails IN ANY ORDER. Then why are we doing arrangements? Because arrangements rely on relative ordering right?
Since the probability of head is 1/2 and tails is also 1/2, wouldn’t we just have 1/2^10 for both A and B?

2

Since it is mentioned in any order, will the number of different order not affect the final result. If there are multiple orders, then what will happen to the probability?