What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards?
B. (4C1 * 4C1) / 52C2
C. 4/52 * 4/51
D. 8C2 / 52 C 2
E. (8 * 7) / 52C2
Where are these questions from? Two things:
* the GMAT will *never* ask questions about standard decks of cards, since people who play bridge or poker would have a substantial (and unfair) advantage over people who do not;
* the GMAT will *never* use notation like '52C2' in an answer choice. That's not even a standard notation in general mathematics; it's more a convenient shorthand to use in internet forums. GMAT answer choices will always be written either as numbers, or using factorials
So that makes me wonder what the source is for these questions, and whether it contains a lot of other irrelevant material.
In any case, there are 4 Kings and 4 Queens in a standard deck. We need our first card to be one of these 8; there is an 8/52 probability our first card is from this group. Then when we pick the second card, we will be picking from 51 cards in total, and there will be 4 left which are of the type we need (if we picked a King first, we need one of the four Queens and vice versa), so there is a 4/51 probability the second card is the right type, and the answer is (8/52)(4/51).
That is equal to answer choice B, though you'd never see anything that looks like answer choice B on the GMAT. It's a bit absurd to write '4C1' in that answer choice anyway, since '4C1' is just equal to 4.
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