Question

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

Answer 1

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

Answer 2

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.