Basic Probability (Deck of Cards)

Question

3. Shuffle a standard deck of 52 cards thoroughly (so that all 52! possible orderings are equally likely.) Then deal the top 4 cards, in order. Find the probability that:

(a) all 4 cards are red

First off, I don't even know how many red cards are there in a standard deck of 52 cards. And I guess since it is supposed to be in order, I am suppose to use permutation?

Answer 1

First off, I don't even know how many red cards are there in a standard deck of 52 cards.

In a standard deck, there are 52 cards divided evenly into the four suits: $\color{red}{\heartsuit, \diamondsuit,} \spadesuit, \clubsuit$.   So half of those 52 are red.

And I guess since it is supposed to be in order, I am suppose to use permutation?

Well, you could, but order doesn't really matter here.   You just want the probability for selecting 4 from among the red cards, when selecting any 4 from the 52 cards.

Since $^n\mathrm C_r$ or $\binom nr$ counts the ways to select $r$ items from a set of $n$, just use that.