Combinations : GMAT Problem Solving (PS)
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# Combinations

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Manager
Joined: 29 Oct 2009
Posts: 201
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
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Kudos [?]: 88 [0], given: 12

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21 Mar 2010, 21:03
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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

CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 3457 [0], given: 360

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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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Senior Manager
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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
henc E is the answer
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Manager
Joined: 29 Oct 2009
Posts: 201
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
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Kudos [?]: 88 [0], given: 12

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22 Mar 2010, 06:07
E is OA.
Thank you for the explanations.
Senior Manager
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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.
Re: Combinations   [#permalink] 22 Mar 2010, 08:02
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