SOLUTION: Hello, this is the second question that I have from the assignment. Five cards are drawn from a standard deck of 52 cards. How many hands of five cards have at least one red

Question 945889: Hello, this is the second question that I have from the assignment.

Five cards are drawn from a standard deck of 52 cards. How many hands of five cards have at least one red card?
This seems like it would be too easy and I think I'm just overthinking it.
Thank you in advance whoever you are.
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
Five cards are drawn from a standard deck of 52 cards. How many hands of five
cards have at least one red card?

First we calculate how many 5-card hands there are whether they contain
red cards or not.

That's 52C5

Next we calculate how many 5-card hands we DO NOT want to count.
We do not want to count any hands that DO NOT contain any red cards,
that is, the 5-card hands that contain only 5 black cards.  There are
26 black cards.

That's 26C5 hands that we DO NOT want to count.  So we subtract them,
and all the rest must contain at least 1 red card.

Answer 52C5-26C5 = 2598960-65780 = 2533180

This procedure of calculating ALL possibilities and then subtracting 
the ones that you DO NOT want will usually be used when you see 
the words "at least one".
.
Edwin

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