What is theoretical probability of being dealt exactly two 8

What is theoretical probability of being dealt exactly two 8\'s in a 5 -card hand from a standard 52 card deck?

Solution

We can deal two 8\'s in [((5),(2))=10] ways. So we have dealt two 8\'s and there are 48 cards remaining from which we need to choose 3 (48 because we musn\'t choose another 8 so 52 cards - 4 8\'s = 48) which we can do in [((48),(3))=17296] ways.

Also total number of all 5-card combinations we can deal from deck of 52 cards is [((52),(5))=2598960] .

So probability of being dealt exactly two 8\'s in a 5-card hand from a standard 52 card deck is [P=(((5),(2))((48),(3)))/(((52),(5)))=(10cdot17296)/2598960approx0.0665497]