Answer:
Explanation:
There are two different techniques that I can think of for arriving at the answer. The first method utilizes combination, sometimes referred to as the “choose” operator. First, we need to know how many 6 cards hands are possible, which can be calculated using 52 choose 6, which in notation looks like (526) =20,358,520 . This is our denominator.
Now that we know how many total 6 cards hands there are in a normal deck, we need to find the numerator, which is how many 6-card hands can be made up of all hearts. Since there are 13 hearts in the deck, we can find that number with (136) =1,716 .
Completely written out in mathematical notation, the probability of drawing 6 cards that are all hearts, appears as follows:
(136)(526)=171620358520≈0.0000843≈0.00843%
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The second method that results in the same value can be found by multiplying together the chances of drawing the individual cards at each step, for example, there is a 1352 chance of the first card drawn being a heart, 1251 for the second, and so on.
This second method looks like:
1352×1251×1150×1049×948×847≈0.0000843≈0.00843
Incidentally, 13!46!7!52! is another way to notate this second method.
Personally, I find the first method to be cleaner and easier to work with, but some may find the second more intuitive.