Probability

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rajatvmittal: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sat Feb 11, 2012 5:01 am; Thanked: 2 times

by rajatvmittal » Wed Oct 10, 2012 8:26 am

A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only. How many different games are possible?

Last edited by rajatvmittal on Wed Oct 10, 2012 8:35 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Wed Oct 10, 2012 8:26 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Oct 10, 2012 8:35 am

rajatvmittal wrote:A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only

I think you're missing part of the question (and the 5 answer choices)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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rajatvmittal: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sat Feb 11, 2012 5:01 am; Thanked: 2 times

by rajatvmittal » Wed Oct 10, 2012 8:44 am

Thanks!

Updated the questions... No answers choices!

Rajat

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Oct 10, 2012 8:55 am

rajatvmittal wrote:A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only. How many different games are possible?

Note: The question is somewhat ambiguous. I'm assuming that the scenarios for each level are considered different. For example, completing scenario B at level 2 is different from completing scenario B at level 3.

Take the task of playing a game (i.e., complete all 5 levels) and break it into stages.

Stage 1: Complete level 1
There are 3 scenarios to choose from, so this stage can be accomplished in 3 ways.

Stage 2: Complete level 2
There are 4 scenarios to choose from, so this stage can be accomplished in 4 ways.

Stage 3: Complete level 3
There are 4 scenarios to choose from, so this stage can be accomplished in 4 ways.

Stage 4: Complete level 4
There are 4 scenarios to choose from, so this stage can be accomplished in 4 ways.

Stage 5: Complete level 5
There are 4 scenarios to choose from, so this stage can be accomplished in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete all 5 stages (and thus complete all 5 levels) in (3)(4)(4)(4)(4) ways ([spoiler]= 768 ways[/spoiler])

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

Brent Hanneson - Creator of GMATPrepNow.com

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rajatvmittal: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sat Feb 11, 2012 5:01 am; Thanked: 2 times

by rajatvmittal » Wed Oct 10, 2012 9:09 am

Thanks Brent..

I thought the same. But your assumption was useful. As answer to the problem was 19. I think if the assumption is changed the answer will be 19.

rajat

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