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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Permutation/Combination - Simple one tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 7 member replies ## Permutation/Combination - Simple one A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible? 45 81 90 10!/2! 10! when they say different color combinations does that mean fro instance red exterior and blue interior and blue exterior and red interior are the same? colors are obviously on different parts of car but the combinations of blue and red is only 1 FYI - answer is 90 so i assume they meant 10 *9 but could easily see how someone would pick (10*9)/2 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12677 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 J N wrote: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible? 45 81 90 10!/2! 10! when they say different color combinations does that mean fro instance red exterior and blue interior and blue exterior and red interior are the same? colors are obviously on different parts of car but the combinations of blue and red is only 1 FYI - answer is 90 so i assume they meant 10 *9 but could easily see how someone would pick (10*9)/2 The correct answer (90) indicates that a car with red exterior and blue interior is different from a car with blue exterior and red interior. Here's one approach: Take the task of choosing colors break it into stages. Stage 1: Choose the exterior color Since there are 10 color choices, we can complete this stage in 10 ways Stage 2: Choose the interior color At this point, we can't choose the color that was used for the exterior. So, we have 9 color options remaining, which means we can complete this stage in 9 ways By the Fundamental Counting Principle (FCP) we can complete the 2 stages (and thus design the car) in (10)(9) ways (= 90 ways) Cheers, Brent Aside: For more information about the FCP, we have a free video on the subject: http://www.gmatprepnow.com/module/gmat-counting?id=775 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! Newbie | Next Rank: 10 Posts Joined 27 Sep 2010 Posted: 1 messages J N wrote: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible? 45 81 90 10!/2! 10! when they say different color combinations does that mean fro instance red exterior and blue interior and blue exterior and red interior are the same? colors are obviously on different parts of car but the combinations of blue and red is only 1 FYI - answer is 90 so i assume they meant 10 *9 but could easily see how someone would pick (10*9)/2 When they say different color combinations - Red Exterior/Blue Interior and Blue Ext/Red Int are 2 different combinations. Thus, a simple way of solving can be: The exterior color can be chosen in 10 different ways. For each exterior color the interior color can be chosen in 9 different ways (Excluding the 1 color, which is used as exterior color) Hence, the total number of ways will be = The number of ways Exterior color can be chosen * The number of ways interior color can be chosen = 10 * 9 = 90 Cheers, True Legendary Member Joined 18 Jun 2012 Posted: 512 messages Followed by: 19 members Upvotes: 42 Test Date: October '13 Target GMAT Score: 740 Brent, what if we add a restriction in this question that says that "Order of colors isnt important" than is the answer 45? _________________ Work hard in Silence, Let Success make the noise. If you found my Post really helpful, then don't forget to click the Thank/follow me button. Senior | Next Rank: 100 Posts Joined 19 Dec 2010 Posted: 51 messages Followed by: 2 members Upvotes: 11 Hi Sana, before Brent answers that question, I'd like to understand for my own self, what you mean by order of colors here. sana.noor wrote: Brent, what if we add a restriction in this question that says that "Order of colors isnt important" than is the answer 45? _________________ If you appreciated my post or even just my time trying to help, please don't forget to click on 'Thanks' and say "Piece o' Cake mate" at the same time. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12677 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 sana.noor wrote: Brent, what if we add a restriction in this question that says that "Order of colors isnt important" than is the answer 45? Yes, the answer would then be 45. The question would simplify to choosing two colors from ten colors. Since the order of the selected colors does not matter (e.g., a car with red exterior and blue interior is THE SAME as a car with blue exterior and red interior), we can use combinations. We can select 2 colors from 10 colors in 10C2 ways (45 ways) Aside: If anyone is interested, we have a free video on calculating combinations (like 10C2) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789 Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! Legendary Member Joined 18 Jun 2012 Posted: 512 messages Followed by: 19 members Upvotes: 42 Test Date: October '13 Target GMAT Score: 740 jitsy wrote: Hi Sana, before Brent answers that question, I'd like to understand for my own self, what you mean by order of colors here. sana.noor wrote: Brent, what if we add a restriction in this question that says that "Order of colors isnt important" than is the answer 45? in permutation "order of selected thing" matter but in combination order of selected thing doesnt matter. for example: AB and BA is counted two different things in permutation because order is important. AB and BA is considered two distinct things. but in combination AB and BA is same thing because order isnt important. if u have selected AB then you cant select BA. _________________ Work hard in Silence, Let Success make the noise. If you found my Post really helpful, then don't forget to click the Thank/follow me button. Senior | Next Rank: 100 Posts Joined 19 Dec 2010 Posted: 51 messages Followed by: 2 members Upvotes: 11 Hi Sana, thanks. Sorry I had meant I do understand the concept of order in P&C but could not relate it to this question since I was thinking of it in the literal 'order' sense when its actually an interior exterior swap. But I realised what you meant when Brent explained. Thanks again sana.noor wrote: jitsy wrote: Hi Sana, before Brent answers that question, I'd like to understand for my own self, what you mean by order of colors here. sana.noor wrote: Brent, what if we add a restriction in this question that says that "Order of colors isnt important" than is the answer 45? in permutation "order of selected thing" matter but in combination order of selected thing doesnt matter. for example: AB and BA is counted two different things in permutation because order is important. AB and BA is considered two distinct things. but in combination AB and BA is same thing because order isnt important. if u have selected AB then you cant select BA. _________________ If you appreciated my post or even just my time trying to help, please don't forget to click on 'Thanks' and say "Piece o' Cake mate" at the same time. Junior | Next Rank: 30 Posts Joined 08 Oct 2012 Posted: 12 messages Followed by: 1 members Upvotes: 2 I computed by getting all possible combinations 10 x 10 = 100; and then subtracting the same colored pairs,which is 10 100-90 = 10 I think that would be clearer for you to avoid confusion. Legendary Member Joined 07 Aug 2014 Posted: 510 messages Followed by: 5 members Upvotes: 3 Hi Brent , One doubt, why did you do till stage2 as we have 10 interior colors are identical to the ten exterior colors and we have to make different combination so should not be 10X9X8X7X.......X1 = 10! Please correct me if i am wrong. Thanks, Shreyans ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12677 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 j_shreyans wrote: Hi Brent , One doubt, why did you do till stage2 as we have 10 interior colors are identical to the ten exterior colors and we have to make different combination so should not be 10X9X8X7X.......X1 = 10! Please correct me if i am wrong. Thanks, Shreyans Hi Shreyans, Once we have selected a color for the exterior (which we can do in 10 ways), we must select a color for the interior. Since we can't repeat the same color, we now have only 9 colors to choose from. That's it. Aside: 10! = 3.6 million. If you were to start listing all of the possible 2-color combinations, you'd soon realize that there can't be 3.6 million possibilities. Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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