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# An entrepreneurship competition requires registering teams to have 3

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Math Expert
Joined: 02 Sep 2009
Posts: 53738
An entrepreneurship competition requires registering teams to have 3  [#permalink]

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26 May 2016, 12:33
00:00

Difficulty:

65% (hard)

Question Stats:

61% (02:27) correct 39% (02:33) wrong based on 109 sessions

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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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Joined: 12 Mar 2013
Posts: 240
An entrepreneurship competition requires registering teams to have 3  [#permalink]

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Updated on: 06 Mar 2018, 10:26
1
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

P(at least one Tech)= p(total) - P( no tech)

=13c3 - 9c3

=286 - 84

= 202 (E)
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We Shall Overcome... One day...

Originally posted by nahid78 on 26 May 2016, 14:27.
Last edited by nahid78 on 06 Mar 2018, 10:26, edited 1 time in total.
Manager
Joined: 29 Nov 2011
Posts: 92
An entrepreneurship competition requires registering teams to have 3  [#permalink]

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28 May 2016, 06:55
nahid78 wrote:
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

P(at least one Tech)= p(total) - P( no tech)

=13c3 - 9c3

=198 (ans D )

calculation seems to be wrong .. its 202 i guess

i put it differently
4C1 *9C2 + 4C2*9C1 + 4C3 = 202
Manager
Joined: 18 May 2016
Posts: 67
Concentration: Finance, International Business
GMAT 1: 720 Q49 V39
GPA: 3.7
WE: Analyst (Investment Banking)
An entrepreneurship competition requires registering teams to have 3  [#permalink]

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28 May 2016, 07:24
1
We have 3 scenarios here:

1) 1 tech & 2 businessmen: 4C1 x 9C2 = 144
2) 2 tech & 1 businessman: 4C2 x 9C1 = 54
3) 3 tech & 0 businessmen: 4C3 = 4

Total: 144+54+4 = 202

Are there any shortcuts to avoid doing all the scenarios separately?
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Joined: 18 Jan 2010
Posts: 251
An entrepreneurship competition requires registering teams to have 3  [#permalink]

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28 May 2016, 08:53
2
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
Intern
Joined: 29 Dec 2016
Posts: 27
Location: India
Concentration: Finance
WE: Supply Chain Management (Energy and Utilities)
Re: An entrepreneurship competition requires registering teams to have 3  [#permalink]

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05 Mar 2018, 08:29
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

I initially did 4C1*12C2 (=264), which is not in the options; therefore, used 13C3-9C3 (=202), which is the correct answer.

Not sure what I am doing wrong with the first method. Can someone tell me what i am doing wrong with 4C1*12C2??

Regards,
Louis
Director
Joined: 14 Nov 2014
Posts: 626
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: An entrepreneurship competition requires registering teams to have 3  [#permalink]

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05 Mar 2018, 09:00
1
louisbharnabas wrote:
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

I initially did 4C1*12C2 (=264), which is not in the options; therefore, used 13C3-9C3 (=202), which is the correct answer.

Not sure what I am doing wrong with the first method. Can someone tell me what i am doing wrong with 4C1*12C2??

Regards,
Louis

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 .
Intern
Joined: 29 Dec 2016
Posts: 27
Location: India
Concentration: Finance
WE: Supply Chain Management (Energy and Utilities)
Re: An entrepreneurship competition requires registering teams to have 3  [#permalink]

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05 Mar 2018, 09:07
sobby wrote:
louisbharnabas wrote:
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

I initially did 4C1*12C2 (=264), which is not in the options; therefore, used 13C3-9C3 (=202), which is the correct answer.

Not sure what I am doing wrong with the first method. Can someone tell me what i am doing wrong with 4C1*12C2??

Regards,
Louis

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 .

Dear Sobby,

Oh yes. You are right. Now i understand.

Thank you.

Regards,
Louis
Re: An entrepreneurship competition requires registering teams to have 3   [#permalink] 05 Mar 2018, 09:07
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# An entrepreneurship competition requires registering teams to have 3

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