Mr. ricketts is randomly distributing 25 hot chocolates and 20 iced coffees to his fellow board members. what is the probability that the first cup he hands out will be hot chocolate and the second cup will be an iced coffee

There are 25 hot chocolates.
There are 20 iced coffees.
Total number of objects = 25 + 20 = 45.

Assume that each object has the same probability of being selected.
The probability of selecting hot chocolate is 25/45 = 5/9.

After selecting hot chocolate, 44 objects remain.
The probability of selecting iced coffee is 20/44 = 5/11

The two selections are independent events. Therefore the probability of selecting hot chocolate followed by iced coffee is
(5/9)*(5/11) = 25/99

25/99

Yea they are simplyfiy the ratios