The face cards are 4 kings, 4 queens, and 4 jacks, which is equal to 12 face cards.
A deck of cards = 52
Now, the probability is given by the next formula:
[tex]P=\frac{\#\text{ of f}avorable\text{ outcomes}}{Total\text{ of outcomes}}[/tex]In fact, we don't have any orders or replacements.
Therefore:
[tex]P=\frac{12C6}{52C6}[/tex]The number of favorable outcomes is 12 chose 6 because we are getting 6 cards.
The total number of outcomes is 52 chose 6 because we have drawn 6 cards from the deck.
C means the combination and is calculated by the next formula :
[tex]n\text{Cr}=\frac{n!}{r!(n-r)!}[/tex]For 12C6:
[tex]12C6=\frac{12!}{6!(12-6)!}=924[/tex][tex]52C6=\frac{52!}{6!(52-6)!}=20358520[/tex]Then:
[tex]P=\frac{154}{221}[/tex]
