If 4 cards are drawn randomly from the standard deck of 52 cards, what is the probability that all 4 cards are red cards?

How would I set this up?

there are 26 red cards
So I would take 26/52
and 48/52?

If this is correct, would I multiply them?

Thanks

The order does not matter, so this is a "combination" problem

Number of possible 4 cards from the reds
= C(26,4) or 26!/(22!4!)
number of possible 4 cards from all
= C(52,4) or 52!/(48!4!)

prob(your event = C(26,4)/C(52,4)
= 14950/270725
= 46/833
= appr .055

Or, consider drawing 4 cards with no replacement. Then the probability of getting all reds is

26/52 * 25/51 * 24/50 * 23/49 = 0.05522

Note that
C(26,4) = 26*25*24*23
C(52,4) = 52*51*50*49

You can see that the division shown by Reiny produces the same fractions.

To find the probability that all 4 cards drawn are red cards, you would indeed multiply the probabilities together.

To set up the problem, you need to consider that each time you draw a card, there are fewer cards left in the deck. The total number of cards decreases by 1 after each draw.

The probability of drawing a red card on the first draw is 26/52 because there are 26 red cards out of the total 52 cards.
After the first red card is drawn, there are now 25 red cards left out of the remaining 51 cards.

Therefore, the probability of drawing a second red card is 25/51.

Following the same logic, the probability of drawing a third red card would be 24/50, and the probability of drawing the fourth red card would be 23/49 since there would be 23 red cards left out of the remaining 49 cards.

To find the overall probability, you multiply these probabilities together:
(26/52) * (25/51) * (24/50) * (23/49) = 0.0588, which is approximately 5.88%.

So the probability that all four cards drawn are red cards is approximately 5.88%.