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# In how many ways can a committee of four men and five women be formed from a group of seven men and seven women? How many different committees can be formed from 5 professors and 15 students if each committee is made up of 2 professors and 10 students?

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1. If there are seven men to choose from and four will be chosen, then the number of ways of choosing the men is $_7C_4=35$. If there are seven women to choose from and five will be chosen, then the number of ways of choosing the women is $_7C_5=21$. The number of ways of choosing four men and five women from a group of seven men and seven women is then $35\cdot21=735$.

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