Two cards are randomly pulled out of a standard pack of 52 cards. What is the probability that both are face cards?
A. 9/169
B. 12/221
C. 33/676
D. 11/221

Work Shown:

For any given suit, there are 3 face cards: Jack, Queen, King.

There are 4 suits, leading to 4*3 = 12 face cards out of 52 total.

The probability of pulling out a face card is 12/52.

After that card is selected, we have 12-1 = 11 face cards left and 52-1 = 51 cards left overall. This is assuming a replacement is not made, or the card is not put back.

The probability of getting another face card, given the first selection was a face card, is 11/51.

Multiplying the two fractions gives:

P(2 face cards) = P(1st facecard)*P(2nd facecard given 1st facecard)

P(2 face cards) = (12/52)*(11/51)

P(2 face cards) = (12*11)/(52*51)

P(2 face cards) = (3*4*11)/(13*4*3*17)

P(2 face cards) = (11)/(13*17)

P(2 face cards) = 11/221