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

Step 1 ：Suppose that 7 cards are drawn from a well-shuffled deck of 52 cards. We want to find the probability that all 7 are hearts.

Step 2 ：The total number of ways to draw 7 cards out of 52 is given by the combination formula '52 choose 7', which equals to 133784560.

Step 3 ：The number of ways to draw 7 hearts out of the 13 hearts in the deck is given by '13 choose 7', which equals to 1716.

Step 4 ：The probability of drawing 7 hearts is then the ratio of '13 choose 7' to '52 choose 7', which is \(\frac{1716}{133784560}\).

Step 5 ：Calculating the above expression, we get approximately 1.2826592246519329e-05.

Step 6 ：Final Answer: The probability that all 7 cards drawn from a well-shuffled deck of 52 cards are hearts is approximately \(\boxed{1.2826592246519329 \times 10^{-5}}\).