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A student-faculty committee consisting of 6 members is to be chosen from a pool of candidates consisting of 5 students and 7 faculty members. The committee must have at least 2 student members and at least 1 faculty member. How many possibilities are there

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okpalawalter8

Answer:

[tex]T=812[/tex]

Step-by-step explanation:

From the question we are told that:

No. Committee Members [tex]n=6[/tex]

Pool of : 5 students and 7 faculty members

At least 2 student members and at least 1 faculty member

Generally the committee is mathematically given by

The Total Events are

[tex]T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)[/tex]

[tex]T=350+350+105+7[/tex]

[tex]T=812[/tex]

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