Hello, Ashwin!

I had to "draw a picture" to understand this one . . .

There are, of course, 52 cards in the deck.How many ways are there to choose 4 cards of different suits

and different values from a deck of 52 cards?

. .

The first card can be any of the 52 cards.

. . Suppose it is

Then these choices remain for the second card:

. .

There are 36 choices for the second card.

Suppose the second card is

Then these choices remain for the third card:

. .

There are 22 choices for the third card.

Suppose the third card is

Then these choices remain for the fourth card:

. .

There are 10 choices for the fourth card.

Disgarding the order in which the four cards are drawn,

. . there are: . such 4-card hands.