8 cards are selected with replacement from a pack of standard 52 cards. How many sequences will contain 3 picture cards, 3 odd cards and 2 even cards?

Question

I need the working. The answer is 3.097 x 10^12. Thanks.

Answer 1

To select 3 picture cards: (12)³ = 1728

To select 3 odd cards (3,5,7 or 9): (16)³ because there are four odds in each of the four suits = 4096

To select 2 even cards (2, 4, 6, 8, 10): (20)² because there are five evens in each of the four suits = 400.

 

The answer desired is the product of these three numbers: 1728(4096)(400) = 2,831,155,200

 

My answer is based on these reasonable assumptions: Ace is neither odd nor even and picture cards are neither odd nor even.

 

I do not get the same as the quoted answer; I would like to see everyone's comment on this question.