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# A retirement plan for a company allows employees to invest in 10 diffe

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Manager
Joined: 29 Oct 2009
Posts: 194
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
A retirement plan for a company allows employees to invest in 10 diffe [#permalink]

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21 Mar 2010, 21:03
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:25) correct 45% (01:06) wrong based on 30 sessions

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A retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that atleast 3 of Sam's 4 funds grew by at least 10% over the last year?

A. 6C3/10C4
B. 6C3.4C1/10C4
C. 6C3.4C1+6C4/10P4
D. 6P3.4P1/10C4
E. 6C3.4C1+6C4/10C4
[Reveal] Spoiler: OA
CEO
Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: A retirement plan for a company allows employees to invest in 10 diffe [#permalink]

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21 Mar 2010, 21:38
E

1) 3 out of 6 ">=10%" funds and 1 out of 4 "<10%" funds: $$C^6_3*C^4_1$$

2) 4 out of 6 ">=10%" funds and 0 out of 4 "<10%" funds: $$C^6_4*C^4_0 = C^6_4$$

3) the total number of possible selections: $$C^{10}_4$$

4) the probability is: $$\frac{C^6_3*C^4_1+C^6_4}{C^{10}_4}$$
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Manager
Joined: 13 Dec 2009
Posts: 248
Re: A retirement plan for a company allows employees to invest in 10 diffe [#permalink]

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21 Mar 2010, 21:49
A retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that atleast 3 of Sam's 4 funds grew by at least 10% over the last year?

A. 6C3/10C4
B. 6C3.4C1/10C4
C. 6C3.4C1+6C4/10P4
D. 6P3.4P1/10C4
E. 6C3.4C1+6C4/10C4

No of ways sam can select 4 funds = 10C4
no of ways he can select all 4 of those funds which grew by 10% =6C4
no of ways he can sleect 4 funds out of 3 of those funds which grew by 10% = 6C3*4C1
so probablity is = (6C3*4C1+6C4)/10C4
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Manager
Joined: 29 Oct 2009
Posts: 194
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Re: A retirement plan for a company allows employees to invest in 10 diffe [#permalink]

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22 Mar 2010, 06:07
E is OA.
Thank you for the explanations.
Senior Manager
Joined: 01 Feb 2010
Posts: 251
Re: A retirement plan for a company allows employees to invest in 10 diffe [#permalink]

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22 Mar 2010, 08:02
A retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that atleast 3 of Sam's 4 funds grew by at least 10% over the last year?

A. 6C3/10C4
B. 6C3.4C1/10C4
C. 6C3.4C1+6C4/10P4
D. 6P3.4P1/10C4
E. 6C3.4C1+6C4/10C4

Three funds with over 10% returns = 6C3
One fund with less than 10% returns = 4C1

Four funds with over 10% returns = 6C4

P = (6C3*4C1 + 6C4)/10C4 hence E.
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Joined: 09 Sep 2013
Posts: 14142
Re: A retirement plan for a company allows employees to invest in 10 diffe [#permalink]

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29 May 2017, 00:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A retirement plan for a company allows employees to invest in 10 diffe   [#permalink] 29 May 2017, 00:33
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