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Omni-MATH / A subset of a student group is called an [i]ideal company[/i] if

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A subset of a student group is called an [i]ideal company[/i] if 1) in this subset, all girls are liked by all young men, 2) no one can be added to this subset without violating condition 11. In a certain group, 99 female students and 1515 students study. Warden of the group made a list of all kinds of ideal companies in this group. What is the largest number of companies on this list?
Plain-text mathematical notation (without MathML)
A subset of a student group is called an [i]ideal company[/i] if
1) in this subset, all girls are liked by all young men,
2) no one can be added to this subset without violating condition 1.
In a certain group, 9 female students and 15 students study. Warden of the group made a list of all kinds of ideal companies in this group. What is the largest number of companies on this list?
Original LaTeX notation
A subset of a student group is called an [i]ideal company[/i] if
1) in this subset, all girls are liked by all young men,
2) no one can be added to this subset without violating condition $1$.
In a certain group, $9$ female students and $15$ students study. Warden of the group made a list of all kinds of ideal companies in this group. What is the largest number of companies on this list?

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