How many girls have black hair?












0












$begingroup$


We have a group of $57$ peoples. $35$ of them are girls. $30$ of them have black hair. How many girls, at least, have black hair?



I have immediately thought to the principle of inclusion-exclusion to answer but first I did very simple reasoning but I do not know if it is correct. Since we don't want to know the exact number of girls: $52$ peoples $-$ $35$ girls = $22$ boys. In the worst case, all the boys have black hair, but since there are only $22$ of them, $13$ girls are left with black hair. Can such an answer be reasonable? If it's wrong, why?






combinatorics







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$endgroup$












  • $begingroup$
    You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
    $endgroup$
    – N. F. Taussig
    Jan 19 at 12:30
















0












$begingroup$


We have a group of $57$ peoples. $35$ of them are girls. $30$ of them have black hair. How many girls, at least, have black hair?



I have immediately thought to the principle of inclusion-exclusion to answer but first I did very simple reasoning but I do not know if it is correct. Since we don't want to know the exact number of girls: $52$ peoples $-$ $35$ girls = $22$ boys. In the worst case, all the boys have black hair, but since there are only $22$ of them, $13$ girls are left with black hair. Can such an answer be reasonable? If it's wrong, why?






combinatorics







share|cite|improve this question











$endgroup$












  • $begingroup$
    You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
    $endgroup$
    – N. F. Taussig
    Jan 19 at 12:30














0












0








0





$begingroup$


We have a group of $57$ peoples. $35$ of them are girls. $30$ of them have black hair. How many girls, at least, have black hair?



I have immediately thought to the principle of inclusion-exclusion to answer but first I did very simple reasoning but I do not know if it is correct. Since we don't want to know the exact number of girls: $52$ peoples $-$ $35$ girls = $22$ boys. In the worst case, all the boys have black hair, but since there are only $22$ of them, $13$ girls are left with black hair. Can such an answer be reasonable? If it's wrong, why?






combinatorics







share|cite|improve this question











$endgroup$




We have a group of $57$ peoples. $35$ of them are girls. $30$ of them have black hair. How many girls, at least, have black hair?



I have immediately thought to the principle of inclusion-exclusion to answer but first I did very simple reasoning but I do not know if it is correct. Since we don't want to know the exact number of girls: $52$ peoples $-$ $35$ girls = $22$ boys. In the worst case, all the boys have black hair, but since there are only $22$ of them, $13$ girls are left with black hair. Can such an answer be reasonable? If it's wrong, why?






combinatorics




combinatorics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 19 at 12:56









idriskameni

755321




755321










asked Jan 19 at 12:16









JackJack

344




344












  • $begingroup$
    You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
    $endgroup$
    – N. F. Taussig
    Jan 19 at 12:30


















  • $begingroup$
    You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
    $endgroup$
    – N. F. Taussig
    Jan 19 at 12:30
















$begingroup$
You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
$endgroup$
– N. F. Taussig
Jan 19 at 12:30




$begingroup$
You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
$endgroup$
– N. F. Taussig
Jan 19 at 12:30










1 Answer
1






active

oldest

votes


















1












$begingroup$

The idea is correct but you made an error.



There are $30$ persons with black hair, so if $22$ of them are boys then $30-22=8$ girls have black hair.



So not $35-22$ as you reasoned wrongly.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
    $endgroup$
    – Jack
    Jan 19 at 12:24










  • $begingroup$
    Yes, it is a good answer and PIE is not needed.
    $endgroup$
    – drhab
    Jan 19 at 12:25











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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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active

oldest

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1












$begingroup$

The idea is correct but you made an error.



There are $30$ persons with black hair, so if $22$ of them are boys then $30-22=8$ girls have black hair.



So not $35-22$ as you reasoned wrongly.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
    $endgroup$
    – Jack
    Jan 19 at 12:24










  • $begingroup$
    Yes, it is a good answer and PIE is not needed.
    $endgroup$
    – drhab
    Jan 19 at 12:25
















1












$begingroup$

The idea is correct but you made an error.



There are $30$ persons with black hair, so if $22$ of them are boys then $30-22=8$ girls have black hair.



So not $35-22$ as you reasoned wrongly.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
    $endgroup$
    – Jack
    Jan 19 at 12:24










  • $begingroup$
    Yes, it is a good answer and PIE is not needed.
    $endgroup$
    – drhab
    Jan 19 at 12:25














1












1








1





$begingroup$

The idea is correct but you made an error.



There are $30$ persons with black hair, so if $22$ of them are boys then $30-22=8$ girls have black hair.



So not $35-22$ as you reasoned wrongly.






share|cite|improve this answer









$endgroup$



The idea is correct but you made an error.



There are $30$ persons with black hair, so if $22$ of them are boys then $30-22=8$ girls have black hair.



So not $35-22$ as you reasoned wrongly.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 19 at 12:23









drhabdrhab

102k545136




102k545136












  • $begingroup$
    Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
    $endgroup$
    – Jack
    Jan 19 at 12:24










  • $begingroup$
    Yes, it is a good answer and PIE is not needed.
    $endgroup$
    – drhab
    Jan 19 at 12:25


















  • $begingroup$
    Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
    $endgroup$
    – Jack
    Jan 19 at 12:24










  • $begingroup$
    Yes, it is a good answer and PIE is not needed.
    $endgroup$
    – drhab
    Jan 19 at 12:25
















$begingroup$
Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
$endgroup$
– Jack
Jan 19 at 12:24




$begingroup$
Yes, you are right :) So, despite my error, could it be a good answer in your opinion?
$endgroup$
– Jack
Jan 19 at 12:24












$begingroup$
Yes, it is a good answer and PIE is not needed.
$endgroup$
– drhab
Jan 19 at 12:25




$begingroup$
Yes, it is a good answer and PIE is not needed.
$endgroup$
– drhab
Jan 19 at 12:25


















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