Question

Suppose that 7 cards are drawn from a? well-shuffled deck of 52 cards. What is the probability that all 7 are heartshearts?

Answer 1

There are 13 hearts in the deck of 52.
If we want to simply choose 7 of them, we use combinatorics, and not permutations.

Thus, the total number of ways to choose 7 of the 13 hearts, is: ¹³C₇ or 1716 ways.
The total in our sample space is simply choosing 7 of the 52 cards, which is: ⁵²C₇ or 133 784 560.

Thus, the probability becomes:
$\frac{1716}{133784560} = \frac{33}{2572780}$