How do I determine the probability I will draw three cards with a value of 8 or higher from a standard deck of cards when drawing five cards?

Question

In this case aces=1, jacks=11, queens=12, kings=13, and jokers are removed from the deck.

Answer 1

There are 6 * 4 = 24 cards that are eight or higher out of a deck of 52 cards (4 8's, 4 9's, 4 10's, 4 J's, 4 Q's, 4 K's).

N = number of items in population = 52

k = number of items that are qualified as successes = 24

n = number of items in sample = 5

x = number of items that qualify as successes = 3

Probability that an n trial hypergeometric experiment results in exactly x successes when the population consists of N items, k of which are classified as successes:

h(x;N,n,k) = C(k,x) * C(N-k,n-x) / C(N,n)

= C(24,3) * C(28,2) / C(52,5)

where C(24,3) is number of combinations of 24 taken 3 at a time = 24! / 21! 3 !

similarly for C(28,2) and C(52,5)