Bunuel wrote:
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
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