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 9 different suits.

Hence, there are 135 cards in the deck with 15 ranks for each of the 9 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?
The number of ways of getting any 5 card hand is

Answer 1

Answer:

Step-by-step explanation:

There are 5 cards we are selecting out of 135 cards so how many ways can we draw 5 cards at a time (w/o replacement)

There are 135 ways to choose the first card.

There are then 134 ways to choose the second card.

There are then 133 ways to choose the third card.

132 to choose the 4th

131 to choose the 5th.

Now multiply those giving 135*134*133*132*131 or you could have just said

135 P 5.

In case you don't know P means permutation.