A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Four cards are pulled in order from this deck of 52 playing cards. What is the probability that the cards will be four spades in a row?
prob of 4 spades
= C(13,4)/C(52,4) = 715/270725
= 11/4165
To calculate the probability of drawing four spades in a row from a standard deck of 52 playing cards, we need to determine the number of favorable outcomes (the number of ways to have four spades in a row) and the total number of possible outcomes (the total number of ways to draw any four cards).
First, let's find the number of ways to have four spades in a row. We know that there are 13 spades in the deck, and we need to find the number of ways to choose four spades in a row. Since the order matters (we want specifically four spades in a row), we can use the concept of permutations:
Number of ways to choose four spades in a row = 1 (because there is only one way to arrange four cards in a specific order)
Next, we need to determine the total number of possible outcomes, which is the number of ways to choose any four cards from a deck of 52 playing cards. Again, since the order matters, we can use permutations:
Total number of possible outcomes = 52 P 4 = 52! / (52 - 4)! = 52! / 48!
Now, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / (52! / 48!)
To get the approximate numerical value of the probability, we can calculate the factorial values in the expression. However, keep in mind that the actual division result may be a large number.