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# 4 professors and 6 students are being considered for a group

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CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
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4 professors and 6 students are being considered for a group [#permalink]  03 Nov 2007, 18:55
4 professors and 6 students are being considered for a group that must consist of 3 people.

A. In how many ways can this group be formed if it has to include at least 1 professor?

B. In how many ways can this group be formed if it has to include 2 professors?

C. In how many ways can this group be formed if it has to include no professors?
Director
Joined: 11 Jun 2007
Posts: 932
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Kudos [?]: 70 [0], given: 0

Re: combos - at least 1 [#permalink]  03 Nov 2007, 19:01
4 professors and 6 students are being considered for a group that must consist of 3 people.

A. In how many ways can this group be formed if it has to include at least 1 professor? total possibilities - all students
10C3 - 6C3 = 120 - 20 = 100

B. In how many ways can this group be formed if it has to include 2 professors? 4C2 * 6C1 = 12*6 = 72

C. In how many ways can this group be formed if it has to include no professors? only students
6C3 = 20
Senior Manager
Joined: 01 Sep 2006
Posts: 302
Location: Phoenix, AZ, USA
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Kudos [?]: 15 [0], given: 0

Re: combos - at least 1 [#permalink]  03 Nov 2007, 19:26
bmwhype2 wrote:
4 professors and 6 students are being considered for a group that must consist of 3 people.

A. In how many ways can this group be formed if it has to include at least 1 professor?
1 professor is must so we need group of 2 from 3 prof and 6 students

1 prof (3C1)+ 1 student (6C1)= 3+6=9
2 prof (3C2) + no student=3
0 prof + 2 students (6C2)=15
9+3+15=27

B. In how many ways can this group be formed if it has to include 2 professors?

Only 1 person needes to be chosen since 2 prof already included

1 prof out of 2 2c1=2 + no students
no prof + 1 student 6C1=6

C. In how many ways can this group be formed if it has to include no professors?

6C3= 6*5*4/6=20
Re: combos - at least 1   [#permalink] 03 Nov 2007, 19:26
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