An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 9 businessmen, how many possible team submissions are possible?

(A) 76
(B) 100
(C) 162
(D) 198
(E) 202
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calculation seems to be wrong .. its 202 i guess

i put it differently
4C1 *9C2 + 4C2*9C1 + 4C3 = 202

At least one Tech member is reqd.
Let us find out the tital ways in which 3 people can be selected (without any restrictions). Then we will find out combination when none of techies is selected.

At least once = (Total - None selected)

Total ways in which a team of 3 can be selected out of 13 persons: 13c3 = \(\frac{13!}{3!10!}\) = \(\frac{11*12*13}{6}\) = 286

Now suppose we dont want to selcet any Tech guy. Now we have to select 3 persons out of 9 persons: 9c3 = \(\frac{9!}{3!6!}\)
= \(\frac{9*8*7}{6}\) = 84

Answer: 286 - 84 = 202. E is the answer

take a simple example:A,B,C and D --4 tech guys
4C1*12C2
A (one mem out of 4) -- BD(two mem out of rest 12 ) --can be a team
B (one mem out of 4) -- AD(two mem out of rest 12) --can also be a team , but both team are same .