Mixing
How many girls have black hair?
$begingroup$
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
edited Jan 19 at 12:56
idriskameni
755321
asked Jan 19 at 12:16
JackJack
344
$endgroup$
add a comment |
$begingroup$
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
edited Jan 19 at 12:56
idriskameni
755321
asked Jan 19 at 12:16
JackJack
344
$endgroup$
$begingroup$
You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
$endgroup$
– N. F. Taussig
Jan 19 at 12:30
add a comment |
$begingroup$
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
edited Jan 19 at 12:56
idriskameni
755321
asked Jan 19 at 12:16
JackJack
344
$endgroup$
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
edited Jan 19 at 12:56
idriskameni
755321
asked Jan 19 at 12:16
JackJack
344
edited Jan 19 at 12:56
idriskameni
755321
asked Jan 19 at 12:16
JackJack
344
edited Jan 19 at 12:56
idriskameni
755321
edited Jan 19 at 12:56
idriskameni
755321
edited Jan 19 at 12:56
idriskameni
755321
755321
asked Jan 19 at 12:16
JackJack
344
asked Jan 19 at 12:16
JackJack
344
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
add a comment |
$begingroup$
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
answered Jan 19 at 12:23
drhabdrhab
102k545136
$endgroup$
$begingroup$
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
add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
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votes
$begingroup$
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.
answered Jan 19 at 12:23
drhabdrhab
102k545136
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered Jan 19 at 12:23
drhabdrhab
102k545136
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered Jan 19 at 12:23
drhabdrhab
102k545136
$endgroup$
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.
answered Jan 19 at 12:23
drhabdrhab
102k545136
answered Jan 19 at 12:23
drhabdrhab
102k545136
answered Jan 19 at 12:23
drhabdrhab
102k545136
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
add a comment |
$begingroup$
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
add a comment |
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$begingroup$
You meant to write $color{red}{57}$ people - $35$ girls $= 22$ boys.
$endgroup$
– N. F. Taussig
Jan 19 at 12:30