How many ways are there to pull 7 cards from a standard deck with the first four being red, the last three being black, and no two ranks can be the same?

Question

Every card has to have a unique rank.

the first four cards must be red, and the last three cards must be black.

This is a counting problem that does not require any combinations or permutations.

Answer 1

Let's let

H = Hearts

D = Diamonds

C = Clubs

S = Spades

Assume order matters. For example 10H, 9H, 8H, 7H, 10C, 9C, 8C is different from 7H, 8H, 9H, 10H, 8C, 9C, 10C

Number of ways:

1st card: 26 (because there are 26 red cards)

2nd card: 24 (because there are 24 remaining possible red cards, as you can't pair with the first card)

3rd card: 22 (similar logic as above)

4th card: 20 (similar logic as above)

5th card: 26 (because there are 26 black cards)

6th card: 24 (because there are 24 remaining possible black cards, as you can't pair with the fifth card)

7th card: 22 (similar logic as above)

Multiply all together: 26*24*22*20*26*24*22