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
Algebra ->
Permutations
-> 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
Log On
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(20056) (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
