Using a standar deck of 52 cards, what is the probability of drawing four cards of the same number(eg.four aces, 4 kings, four 2s, four 3s,etc)?

(4/52)*(3/52)*(2/52)*(1/52)

is this 4 cards of everything?

Let's just take one of the quads, say the kings

prob of 4 kings = (4/52)(3/51)(2/50)(1/49)

but there are 13 of these types
so prob of your event = 13(4/52)(3/51)(2/50)(1/49) = 1/20825

To find the probability of drawing four cards of the same number from a standard deck of 52 cards, we need to determine two things:

1. The number of ways it is possible to get four cards of the same number.
2. The total number of possible outcomes when drawing four cards from the deck.

Let's break it down step by step:

Step 1: Determine the number of ways to get four cards of the same number.
In a standard deck, for each card number (Ace, 2, 3, 4, ..., King), there are four cards (one in each suit - Clubs, Diamonds, Hearts, Spades). So, for each card number, there are 4 different cards that could be drawn. Therefore, for any given number, the number of ways to get four cards of the same number is 4.

Step 2: Determine the total number of possible outcomes.
When drawing four cards from a 52-card deck, the total number of possibilities can be calculated using the combination formula. Since order doesn't matter when drawing the cards, we can use the combination formula C(n, r) = n! / (r! * (n - r)!).

Using this formula, we have:

n = 52 (total number of cards in the deck)
r = 4 (number of cards to be drawn)

So, the total number of possible outcomes when drawing four cards is C(52, 4) = 52! / (4! * (52 - 4)!) = 52! / (4! * 48!) = (52*51*50*49) / (4*3*2*1) = 270,725.

Step 3: Calculate the probability.
Now that we know the number of favorable outcomes (Step 1) and the total number of possible outcomes (Step 2), we can calculate the probability.

The probability of drawing four cards of the same number is given by:

Probability = Number of favorable outcomes / Total number of possible outcomes

So, the probability of drawing four cards of the same number is 4 / 270,725.

Therefore, the probability is approximately 0.001475.