SOLUTION: In how many ways can 8 books be distributed to Mario and Luz, if Mario gets 5 books and Luz 3?
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Question 217319: In how many ways can 8 books be distributed to Mario and Luz, if Mario gets 5 books and Luz 3?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
It appears that the answer would be:
8! / (3!*5!) = 56 ways.
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Assume it was 5 books and Mario gets 3 and Luz gets 2
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Same formula would apply, only the formula would be:
5! / (3!*2!) = 10
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Since the numbers are smaller, it's easier to show.
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Let the books be abcde
Mario gets:Luz gets
abc:de
abd:ce
abe:cd
acd:be
ace:bd
ade:bc
bcd:ae
bce:ad
bde:ac
cde:ab
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Whatever combination Mario gets, Luz gets the rest, and vice versa.
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By himself Mario can get 8! / (3!*5!)
By himself Luz can get 8! / (5!*3!)
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The formula is the same formula for each as it is for both.
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General Formula for number of combinations is n! / ((n-x)!*x!)
If n is 8 and x is 5, this formula becomes:
8! / (3!*5!)
If n is 8 and x is 3, this formula becomes:
8! / (5!*3!)
As you can see, the formula is the same whether x is 5 or 3.
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Your answer is 56 ways.
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That answer is the same if the question was posed as follows:
1. In how many ways can 8 books be distributed to Mario, if Mario gets 5 books at a time?
2. In how many ways can 8 books be distributed to Luz, if Luz gets 3 books at a time?
3. In how many ways can 8 books be distributed to Mario and Luz, if Mario gets 5 books and Luz 3?
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