A typical deck of cards has 4 suits (,,,) - and the following 13 denominations: Ace, 2 thru 10, Jack, Queen, and king). A single card has two characteristics suit and denomination, for example [King of ] or [4 of ] etc.

Imagine a typical deck of cards with an additional 2 suit(s) say: horseshoes and stars. Each new suit still has the normal 13 denominations as the original suits. Your new expanded deck then has 78 total cards and a total of 6 suits.

If 5 cards are randomly selected without replacement from your deck of 78 card deck. Find the probabilities of the following:

a. Three of a kind, meaning three cards with the same denomination and two singular cards who's denomination don't match any other cards in the hand. (If rounding, use at least five decimals in your answer)

b. A flush, meaning all 5 cards are from the same suit. (If rounding, use at least five decimals in your answer)

c. 3 Kings and 2 s .(If rounding, use at least five decimals in your answer)