Question

Two cards are selected from a pack of 52 cards. In how many ways this selection can be done such.

(1) one is a face card and the other is a number card?

(2) both are of different colours? 

(3) both are of same suit?

Answer 1

First of all, in the question let us agree that an Ace card is neither a face card, nor a number card.  And, the question is asking  "how many ways", as opposed to asking about probabilities.

(1) there are 12 face cards and 36 number cards in a deck so there are 12 x 36 = 432 different ways to get one face card and one number card

(2) there are 26 red cards and 26 black cards in a deck of cards so there are 26 x 26 = 676 different ways to get one red card and one black card

(3) there are four suits of 13 cards each so there are 13 x 12 x 4 = 624 different ways to get two cards both of the same suit