# 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?

2
by Mecrin

2015-10-07T13:37:38+05:30

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The 8 members team can be either of the following:
a. 3 professor, 2 technical managers and 3 database expert
Total ways of choosing this =10C3*8C2*10C3=120*28*120=403200

b. 2 professor, 3 technical managers and 3 database expert
Total ways of choosing this =10C2*8C3*10C3=45*56*120=302400

c. 2 professor, 2 technical managers and 4 database expert
Total ways of choosing this =10C2*8C2*10C4=45*28*210=264600

Total ways = 403200+302400+264600 = 970200
Total ways is 970200.
2015-10-07T18:53:24+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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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