# How many different 8 professionals committees can be formed each containing at least 2 Professors, at least 2 Technical Managers and 3 Database Experts from list of 10 Professors, 8 Technical Managers and 10 Database Experts?

1
by MayurTRZ

2015-10-21T15:05:49+05:30

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we have 10 prof. (P),  8 tech. managers(TM),  and 10 DB experts (DBE).

we have to select at least  2 P, 2 TM, and 3 DBE.  That makes up a total of 7.  Then one more person can be a P, TM or DBE.

number of ways of formation of committee
= ways of selecting 3 P +  2 TM + 3 DBE
+ ways of selecting 2 P + 3 TM + 3 DBE
+ ways of selecting 2 P + 2 TM + 4 DBE

= C(10,3) * C(8,2) * C(10,3)
+ C(10,2)* C(8,3) * C(10,3)
+ C(10,2) * C(8,2) * C(10,4)

=   10*9*8/3! * 8*7/2!  * 10*9*8/ 3!
+ 10*9/2! * 8*7*6/3!  * 10*9*8/3!
+ 10*9/2!  * 8*7/2!  *  10*9*8*7/4!

= 560*720 + 420*720 + 45*28* 210
=  970, 200

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