A three-person committee must be chosen from a group of 7 professors and 12 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?  Choose the correct choice from the following choices.
A) A)70  B) B)743  C) C)749  D) D)1,260  E) E)1,980
Total number of ways to select at least one professor = Number of ways to select 3 people from 12 students and 7 professors - Number of ways to select 3 people from 12 student (i.e. without including any professor)   = 197493 - 127493 = 969 - 220= 
<gadget id="calculator">969 - 220</gadget>
<output>749</output>
749   ANSWER:749
<result>C</result>
A three-person committee must be chosen from a group of 7 professors and 12 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?