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# Ben needs to form a committee of 3 from a group of 8

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Manager
Joined: 15 Jul 2004
Posts: 73
Followers: 3

Kudos [?]: 9 [0], given: 0

Ben needs to form a committee of 3 from a group of 8 [#permalink]  06 Apr 2005, 10:04
00:00

Difficulty:

(N/A)

Question Stats:

80% (01:45) correct 20% (01:12) wrong based on 22 sessions
Ben needs to form a committee of 3 from a group of 8 engineers
to study design improvements for a product. If two of the
engineers are too inexperienced to serve together on the
committee, how many different committees can Ben form?

20
30
50
56
336
_________________

===========================
Let us make hay while the sun shines.
Don Quixote. Part i. Book. iii. Chap. xi.

Senior Manager
Joined: 19 Feb 2005
Posts: 487
Location: Milan Italy
Followers: 1

Kudos [?]: 11 [0], given: 0

I'm getting through this by educated guessing...
First: total possible outcomes=8c3=56
so D=56; and E=336 are OUT.
find in how many committees the 2 are together
1*1*6c1=6
so 56-6=50
I learnt the technique of total possible outcomes- unfavorable outcomes in this forum and I'm really grateful to GmatClub

However, Hope it's right!
Director
Joined: 18 Feb 2005
Posts: 674
Followers: 1

Kudos [?]: 2 [0], given: 0

30 ways

The 1 exp guy can be selected in 2C1=2 ways
the rest of the 2 guys can be selected in 6C2 ways
2*6C2 = 30 ways
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5077
Location: Singapore
Followers: 22

Kudos [?]: 186 [0], given: 0

Total number of 3 man team = 8!/3!5! = 56
Total number of teams with 2 inexperienced engineers in the same team = 6!/1!5! = 6
So total number of teams with no 2 inexperienced engineers = 56-6=50

Manager
Joined: 15 Jul 2004
Posts: 73
Followers: 3

Kudos [?]: 9 [0], given: 0

OA is C

_________________

===========================
Let us make hay while the sun shines.
Don Quixote. Part i. Book. iii. Chap. xi.

Manager
Joined: 15 Jul 2004
Posts: 73
Followers: 3

Kudos [?]: 9 [0], given: 0

Could someone write the universal formula for this:

Ben needs to form a committee of X from a group of Y engineers. If Z of the
engineers are too inexperienced to serve together on the
committee, how many different committees can Ben form?

1) Z<X<Y
2) Z<=X<=Y
_________________

===========================
Let us make hay while the sun shines.
Don Quixote. Part i. Book. iii. Chap. xi.

Manager
Joined: 28 Oct 2004
Posts: 95
Location: Irvine, CA
Followers: 1

Kudos [?]: 0 [0], given: 0

just try to think 2 things:

1) total possible outcomes

2) what exception are there, if it is easier to count the exceptions, then we just substract the exceptions from the total outcomes.

this is specially usefull when we are working with outcomes,

when it is about percentages, it is different.

_________________

discipline is what I need.

VP
Joined: 30 Sep 2004
Posts: 1489
Location: Germany
Followers: 4

Kudos [?]: 96 [0], given: 0

gmat2me2 wrote:
30 ways

The 1 exp guy can be selected in 2C1=2 ways
the rest of the 2 guys can be selected in 6C2 ways
2*6C2 = 30 ways

but your reasoning is also correct. you just forgot to add the combinations without the two engineers:

2*6c2 + 6c3 = 50
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

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