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If 3 persons are selected at random from 8 persons for 3 positions pr

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
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If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink]

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15 Sep 2017, 02:04
1
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Difficulty:

35% (medium)

Question Stats:

55% (00:38) correct 45% (00:35) wrong based on 76 sessions

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[GMAT math practice question]

If 3 persons are selected at random from 8 persons for 3 positions present, vice-present, and secretary, how many such ways are possible?

A. 56
B. 70
C. 240
D. 336
E. 1680

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1393 Location: Viet Nam Re: If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink] Show Tags 15 Sep 2017, 05:04 MathRevolution wrote: [GMAT math practice question] If 3 persons are selected at random from 8 persons for 3 positions present, vice-present, and secretary, how many such ways are possible? A. 56 B. 70 C. 240 D. 336 E. 1680 Choose for present position: 8 ways. Choose for vice-present position: 7 ways Choose for secretary position: 6 ways. Total possible ways: 8 * 7 * 6 = 336 ways. Answer D _________________ Manager Joined: 11 Jun 2017 Posts: 80 Re: If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink] Show Tags 15 Sep 2017, 12:20 1 No of possibilities when 3 people are selected out of 8 = 8C3 = 56 Now further, the positions can be arranged in 3! ways = 56*3! = 336 (D) PS Forum Moderator Joined: 25 Feb 2013 Posts: 1144 Location: India GPA: 3.82 Re: If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink] Show Tags 15 Sep 2017, 12:26 MathRevolution wrote: [GMAT math practice question] If 3 persons are selected at random from 8 persons for 3 positions present, vice-present, and secretary, how many such ways are possible? A. 56 B. 70 C. 240 D. 336 E. 1680 Can be solved through Combination, however this is an arrangement question where 8 people need to be arranged in 3 positions. Hence $$8_P_3$$ $$=336$$ Option D SC Moderator Joined: 22 May 2016 Posts: 1765 If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink] Show Tags 15 Sep 2017, 13:57 MathRevolution wrote: [GMAT math practice question] If 3 persons are selected at random from 8 persons for 3 positions present, vice-present, and secretary, how many such ways are possible? A. 56 B. 70 C. 240 D. 336 E. 1680 Order matters. President is like first prize, vice-president is like second prize, and secretary is like third prize. It's a permutation (or use FCP because there are three slots, and 8*7*6 possibilities). $$_{n}P_{k} = \frac{n!}{(n - k)!}$$ $$_8P_3 = \frac{8*7*6*(5!)}{(5!)}$$ = 336 ANSWER D **Long version $$_8P_3 = \frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}$$ = 336 _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5600 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink] Show Tags 17 Sep 2017, 18:46 => 8P3 = 8 x 7 x 6 = 336 Ans: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If 3 persons are selected at random from 8 persons for 3 positions pr [#permalink]

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20 Sep 2017, 15:53
MathRevolution wrote:
[GMAT math practice question]

If 3 persons are selected at random from 8 persons for 3 positions present, vice-present, and secretary, how many such ways are possible?

A. 56
B. 70
C. 240
D. 336
E. 1680

The order of selection is important in this scenario, so this is a permutation problem. The number of ways to select 3 people from 8 for the given positions is 8P3 = 8!/(8-3)! = 8 x 7 x 6 = 336 ways.

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Re: If 3 persons are selected at random from 8 persons for 3 positions pr   [#permalink] 20 Sep 2017, 15:53
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