at least 1 professor

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Mar 30, 2009 5:46 am

4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. In how many ways can this committee be formed if it has to include at least 1 professor?

A. 36
B. 60
C. 72
D. 80
E. 100

OA E

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Source: Beat The GMAT — Problem Solving | Mon Mar 30, 2009 5:46 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Mon Mar 30, 2009 5:53 am

total number of ways in which a committee of 3 people can be chosen out of 10 people is 10C3=120 ways.

number of ways in which a committee of 3 can be chosen out of 6 students (no professors) is 6C3 =20 ways

=> number of ways in which a committee of 3 people will have atleast 1 professor is 120-20 =100 ways

hence E

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