I recently started studying probability from a textbook and in the textbook it gave a detailed breakdown of calculating the probability having a hand of cards (5) and X number of them being aces. however it seems to skip explaining a change in values.
The first step i completely understood:
P(AB)= P(A intersect B) P(B)
Which for this example are these values which make sense to me, 4 combinations of 2, and of the 5 card hand, 3 cards left can be any of the other 48 cards:
However in the next step in the textbook the values change to:
The step on the first line is the part i do not understand:
how has four combinations of 2 (4C2) become:
(4 * 3)/(2*1)
Are they subtracting the combinations from the total number of possible cards to get the 3? and then why multiply the number 2 by 1?
I have looked around online for similar questions to see if they could elaborate on the steps in the textbook however they largely were using a number of different ways to calculate the probability and did not perform this step...