You select 6 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards

Step-by-step 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%  

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.

11/51

Step-by-step explanation: After you've picked the first card, if it's a face card then there are only 11 faces cards left, out of a total of 51. So the probability of the next card also being a face card is 11/51.

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step-by-step explanation: