Question

Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are diamonds?
The probability is
(Round to six decimal places as needed.)

Answer 1

There are 13 diamonds in the deck, so $\dbinom{13}3$ ways of drawing 3 diamonds.

There is a total of $\dbinom{52}3$ ways of drawing any 3 cards from the deck.

So the probability of drawing 3 diamonds is

$\dfrac{\binom{13}3}{\binom{52}3}=\dfrac{11}{850}\approx0.012941$

where $\dbinom nk=\dfrac{n!}{k!(n-k)!}$.