Question

What is the theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52-card deck?

Answer 1

3 fours and evidently 2 not fours

Answer 2

number of ways to get 3 out of the four 4's is 4
number of possibilities for 2 out of the 48 cards that are not four is \(\binom{48}{2}\)

Answer 3

and the total number of 5 card hands in a 52 card deck is \(\binom{52}{5}\)
your answer is
\[\frac{4\times \dbinom{48}{2}}{\dbinom{52}{5}}\]

Answer 4

Do i have to solve that to get my answer ?

Answer 5

i would use a calculator, or better yet use this
https://www.wolframalpha.com/input/?i=%284*%2848+choose+2%29%2F%2852+choose+5%29