Question

Christy draws 3 cards from the deck one at a time without replacement. What is the probability of selecting the cards in the order: diamond, spade and diamond?

Answer 1

Start with a deck of 52 cards. Draw 1 card. Probability of drawing a diamond first:


`\frac{\binom{13}1}{\binom{52}1}`

Now draw another single card from the deck, which now contains 51 cards. Probability of drawing a spade:


`\frac{\binom{13}1}{\binom{51}1}`

Draw 1 last card. The deck has 50 cards left, and 12 of these are diamonds. Probability of drawing a diamond:


`\frac{\binom{12}1}{\binom{50}1}`

So the probability of drawing a diamond, then a spade, then another diamond is


`\frac{\binom{13}1}{\binom{52}1}\cdot\frac{\binom{13}1}{\binom{51}1}\cdot\frac{\binom{12}1}{\binom{50}1}=(13)/(850)`