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The retirement plan for a company allows employees to invest

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The retirement plan for a company allows employees to invest [#permalink] New post 21 Feb 2012, 07:51
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The 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 3 of Sam’s 4 funds grew by at least 10% over last year?

(A) 6C3 / 10C4
(B) 6C3 * 4C1 / 10C4
(C) 6C3 * 4C1 / 10P4
(D) 6P3 * 4P1 / 10C4
(E) 6P3 * 4P1 / 10P4
[Reveal] Spoiler: OA

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Re: The retirement plan for a company allows employees to invest [#permalink] New post 21 Feb 2012, 08:19
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carcass wrote:
The 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 3 of Sam’s 4 funds grew by at least 10% over last year?

(A) 6C3 / 10C4
(B) 6C3 * 4C1 / 10C4
(C) 6C3 * 4C1 / 10P4
(D) 6P3 * 4P1 / 10C4
(E) 6P3 * 4P1 / 10P4

OA later and I would to know how you attach this problem and if is simple or quite difficult.

Thanks GMATClub


\frac{C^3_6*C^1_4}{C^4_{10}}, where C^3_6 is ways to select 3 funds which grew by at least 10% over the last year out of 6 such funds, C^1_4 is ways to select 1 other fund from 4 and C^4_{10} is total ways to select 4 funds out of 10.

Answer: B.
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Re: The retirement plan for a company allows employees to invest [#permalink] New post 21 Feb 2012, 08:24
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Re: The retirement plan for a company allows employees to invest [#permalink] New post 21 Feb 2012, 08:36
Total funds = 10
>10% = 6
<10% = 4

Question: Prob to pick 4 funds (3>10% and 1> 10%)

Option 1: Pick 3 out of 6 = 6C3 = 20
Option 2: Pick 1 out of 4 = 4C1 = 4

Total # = 4C10 = 210

Probability = \frac{Option 1*Option 2}{Total}
or "B"
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Re: The retirement plan for a company allows employees to invest [#permalink] New post 21 Feb 2012, 10:55
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The retirement plan for a company allows employees to invest [#permalink] New post 22 May 2013, 05:50
The 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 3 of Sam's 4 funds grew by at least 10% over last year?

(A) \frac{C^6_3}{C^10_4}
(B) \frac{C^6_3 * C^4_1}{C^(10)_4}
(C)
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Re: The retirement plan for a company allows employees to invest [#permalink] New post 22 May 2013, 05:51
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closed271 wrote:
The 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 3 of Sam's 4 funds grew by at least 10% over last year?

(A) \frac{C^6_3}{C^10_4}
(B) \frac{C^6_3 * C^4_1}{C^(10)_4}
(C)


Merging similar topics. Please refer to the solutions above.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The retirement plan for a company allows employees to invest [#permalink] New post 22 May 2013, 08:39
I know this is a somewhat silly question but I need a confirmation on that

As for options (C) and (D), is it possible to combine a combination and permutation in one question? At first sight I would exclude them because I guess, it would not be logical to solve for a comb and perm. at the same time.

If this is not the case, would you please give examples of when would this be possible?
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Re: The retirement plan for a company allows employees to invest   [#permalink] 22 May 2013, 08:39
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