In a standard deck of cards, there are 52 cards. There are 3 face cards in each suit (King, Queen, Jack) so there are 4*3 or 12 face cards.

There is no indication of how you are picking the 5 cards, so I will show you the solution for each.

Cards drawn and order maintained (Permutation):

The number of ways you can draw five face cards out of the 12 availably is: _{12}P_{5} = 12!/(12-5)! = 95040

The number of ways you can draw five cards (regardless of value) out of the 52 is: _{52}P_{5} = 52!/(52-5)! = 311875200

The likelihood of getting the 5 face cards is: 95040/311875200 ≈ 0.000305.

Cards drawn and simply grouped (Combination): (This is the more plausible interpretation of the question)

The number of ways you can draw five face cards out of the 12 availably is: _{12}C_{5} = 12!/((12-5)!5!) = 792

The number of ways you can draw five cards (regardless of value) out of the 52 is: _{52}P_{5} = 52!/((52-5)!5!) = 2598960

The likelihood of getting the 5 face cards is: 792/2598960 ≈ 0.000305.

(Interestingly, you get the same answer. That usually doesn't happen).

Kate O.

thank you but I'm a little confused, I did 12P5 / 52P5 = 95,040 / 311,875,200, which gave me 3.047x10^-48d