Question

We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 15.
ii) One of 5 different suits.

Hence, there are 75 cards in the deck with 15 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.a)

How many different ways are there to get any 5 card hand?

Answer 1

We have a deck of 75 cards, and we have to select 5 cards out of these 75 cards. The number of ways to get 5 card hand can be obtained by using combination.

The number of Combinations of n objects taken r at a time is:

Hence, number of ways to get 5 card hand =