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A committee of 3 has to be formed randomly from a group of 6 people.

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A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 23 Jul 2010, 08:56
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A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?

A. \(\frac{1}{10}\)
B. \(\frac{1}{5}\)
C. \(\frac{3}{10}\)
D. \(\frac{2}{5}\)
E. \(\frac{1}{2}\)

(C) 2008 GMAT Club - m23#30

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-committee-of-3-has-to-be-formed-randomly-from-a-group-of-81051.html
[Reveal] Spoiler: OA

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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 23 Jul 2010, 11:38
rxs0005 wrote:
A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?



.1

.2

3/10

.4

.5


I think this one is already solved here: probability-a-committee-of-3-has-to-be-formed-81051.html

But anyway, my try:

Assuming that Tom is selected and Ann must not be selected, you get to choose: 4C2 = 6 possibilities, over the total number of possibilities which are 6C3 = 20.

That gives us 6/20 --> 3/10.
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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 02 Aug 2010, 04:00
two ways to solve this kind of problem

way 1. count the number of event needed and number of event available

number of events available is 6*5*4/3*2*1 (set without order-Princeton review). Number is 20

number of events needed is: we take Tom and 2 persons from 4 person. there are 4*3/2 (set without order). number is 6

result is 6/20

way 2: separate into cases, find P of each case and multiple or plus together.

case 1: find P (A and first person and second person)

P1=(1/6)*(4/5)*(3/4)=1/10

case 2, find P (first person and A and second person

P2=(4/6)*(1/5)*(3/4)=1/10

case 3, find P (first person and second person and A)

P3=(4/6)*(3/5)*(1/4)=1/10

P=p1+p2+p3=3/10
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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 02 Aug 2010, 17:14
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[quote="rxs0005"]A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?



.1

.2

3/10

.4

.5

That's a good one.

C (3,6) - all the possible arrangements

C(2,4) is the number of ways the committe with Tom and without Mary.

P = C(2,4)/(C 3,6) = 3/10
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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 02 Aug 2010, 17:22
thangvietnam wrote:
two ways to solve this kind of problem

way 1. count the number of event needed and number of event available

number of events available is 6*5*4/3*2*1 (set without order-Princeton review). Number is 20

number of events needed is: we take Tom and 2 persons from 4 person. there are 4*3/2 (set without order). number is 6

result is 6/20

way 2: separate into cases, find P of each case and multiple or plus together.

case 1: find P (A and first person and second person)

P1=(1/6)*(4/5)*(3/4)=1/10

case 2, find P (first person and A and second person

P2=(4/6)*(1/5)*(3/4)=1/10

case 3, find P (first person and second person and A)

P3=(4/6)*(3/5)*(1/4)=1/10

P=p1+p2+p3=3/10



As you noticed that all 3 probabilities are the same and they are the same for a reason.
Consider this example what is the probablity of selecting the integer 1 out of 4 different numbers, it's 1/4 and what is the probability of selecting 2 out of 4 different numbers, it's also 1/4.

The same principle is applicable to this problem. The order in which you select a person, first, second or third does not matter, the probability is the same.
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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 26 Dec 2011, 23:46
How did you guys come up with 4C2...? I do not understand this step...please enlighten me:)
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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 27 Dec 2011, 03:31
we have 6 people
Tom is always selected so we are left with 2 people to choose from rest 5 people
since marry is never selected so question left is selecting 2 people from rest 4 people
so answer is 4C2/6C3=6/20=3/10
ANS is C
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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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Re: A committee of 3 has to be formed randomly from a group of 6 people. [#permalink]

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New post 03 May 2016, 04:28
Expert's post
rxs0005 wrote:
A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?

A. \(\frac{1}{10}\)
B. \(\frac{1}{5}\)
C. \(\frac{3}{10}\)
D. \(\frac{2}{5}\)
E. \(\frac{1}{2}\)

(C) 2008 GMAT Club - m23#30


You can solve this problem with direct probability approach as well. We need the probability of T, NM, NM (Tom, not Mary, not Mary). \(P(T, NM, NM)=3*\frac{1}{6} * \frac{4}{5} * \frac{3}{4}=\frac{3}{10}\), we are multiplying by 3 since {T, NM, NM} scenario can occur in 3 different ways: {T, NM, NM}, {NM, T, NM}, {NM, NM, T}.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-committee-of-3-has-to-be-formed-randomly-from-a-group-of-81051.html
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Re: A committee of 3 has to be formed randomly from a group of 6 people.   [#permalink] 03 May 2016, 04:28
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