7 cards are drawn from a standard deck of 52 playing cards H

7 cards are drawn from a standard deck of 52 playing cards. How many different 7-card hands are possible if the drawing is done without replacement?

Solution

Here order of selections is not important, so we will use combination.

Number of different hands possible = 52C7 = 52! / (7! * (52 - 7)!) = 133784560 (ans)