Final answer:
The probability of drawing 9 cards of the same suit without replacement is calculated using the combination formula C(13, 9) for one suit, divided by C(52, 9) for the total deck outcome. The combinatoric expression for this probability is P(nine cards of the same suit) = C(13, 9) / C(52, 9).
Step-by-step explanation:
To determine the probability of drawing 9 cards of the same suit without replacement from a standard deck of 52 cards, use combinations. Since each suit has 13 cards, and we want to draw 9 cards of the same suit, we need to calculate the number of combinations of 9 cards from the 13 of a single suit. This is denoted as C(13, 9). The total number of possible outcomes for drawing 9 cards without replacement from the entire deck is the combination C(52, 9).
Thus, the probability P(nine cards of the same suit) is the ratio of the number of ways to draw 9 cards of the same suit to the total number of ways to draw 9 cards from the deck, which is:
P(nine cards of the same suit) = C(13, 9) / C(52, 9)
Remember, the combination formula C(n, k) = n! / (k!(n-k)!), where '!' denotes factorial.
Therefore, your calculation would look something like this:
P(nine cards of the same suit) = 13! / (9!(13-9)!) divided by 52! / (9!(52-9)!)
When you compute the values, you will get the exact probability.