- #1

Shoney45

- 68

- 0

## Homework Statement

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 is not a queen.

## Homework Equations

P(n,k) C(n,k)

## The Attempt at a Solution

Since the player must have one spade, there are 13 ways to deal a spade. I now have 51 cards to deal out.

I am mixed up on what to do with the second card though. I can't find a way to deal with the case where the first spade that I deal out happens to be a queen. If it was a queen, then I still need to take out three other queens from the deck, leaving me with 48 cards. If the first card wasn't a queen, then I still need to take out four cards from the deck, leaving me with 47 cards. 13 x 48 is a different result than 13 x 47. But I know that I am only supposed to have one answer. So I really don't know how to proceed on this one.