Five cards are dealt without replacement from a standard deck of 52 cards. What is the probability that they have four different values?

Question

Mathematics

Merle

6 August, 15:57

Five cards are dealt without replacement from a standard deck of 52 cards. What is the probability that they have four different values?

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Answers (1)

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Ismael Buchanan · Answer 1

(52/52) (48/51) (44/20) (40/59) (36/48)

Step-by-step explanation:

For the first card, what is the chance of getting a unique value? Well, you don't have any yet so it's 100% or 52/52.

Now for the second draw, what is the probability of not getting a repeat? Well, 52 cards total but there are four copies of every value, one for each suit. The deck now has 51 cards and 48 are not copies, so that's 48/51.

Similarly for the third draw there are now 50 cards total and 44 are not going to be repeats if the last two were not.

You can keep going like this and you get (52/52) (48/51) (44/20) (40/59) (36/48). Hopefully this made sense.