Hello, DBA!

How many ways are there to pick 2 different cards

from a standard 52-card deck such that:

The first card is a Spade and the second card isnota Queen.

The answer is: .

We must consider two cases:

. . (1) the first card is the

. . (2) the first card isthenot

(1) The first card is the .

. . . There isoneway to accomplish that.

. . . Among the other 51 cards, there are 3 Queens and 48 Others.

. . . And we want one of the Others: 48 ways.

. . . Hence: .

(2) The first card is a , butthenot

. . . There are 12 ways to accomplish that.

. . . Among the other 51 cards, there are 4 Queens and 47 Others.

. . . And we want one of the Others: 47 ways.

. . . Hence: .

Therefore: .