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17 Oct 2023, 05:05
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Number of possible combinations: 36
Number of vehicles to be displayed: 14
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Difficulty:
95%
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Question Stats:
26% (03:26) correct
74%
(03:25)
wrong
based on 213
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Data Insights (DI) Butler 2023-24 [Question #47, Date: Oct-17-2023]
An auto manufacturer produces two body styles, sedan and convertible, each available in black, white, silver, red, and blue. Upholstery and interiors can be ordered in black, white, red, or blue, but the manufacturer will not put a red interior in a blue body or a blue interior in a red body. For an auto show, the manufacturer wants to display different available combinations to the limit of the space available. Because silver is considered too common, the decision is made not to display any vehicles with silver bodies. The number of remaining combinations is too large for the available space, so the decision is made to display half the interior/exterior color combinations as sedans and half as convertibles. Find the number of vehicle combinations that are actually possible and the number of vehicles that will be displayed.
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| Number of possible combinations | Number of vehicles to be displayed | |
| 14 | ||
| 18 | ||
| 24 | ||
| 28 | ||
| 34 | ||
| 36 |
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Official Answer
Number of possible combinations: 36
Number of vehicles to be displayed: 14
kryinkrumble
Joined: 14 Oct 2023
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Updated on: 18 Oct 2023, 02:45
Originally posted by kryinkrumble on 17 Oct 2023, 23:42.
Last edited by kryinkrumble on 18 Oct 2023, 02:45, edited 2 times in total.
Last edited by kryinkrumble on 18 Oct 2023, 02:45, edited 2 times in total.
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Number of possible combinations = 2*[(4*4)-2] =28 -> There are 4 possible types of exterior colours (excluding silver) and 4 possible types of interior colours and we have to exclude red exterior blue interior and red interior blue exterior. In addition, we have to consider that all these combination can apply for both sedans and convertible.
Number of cars on display = 28/2 = 14 -> decision is to display half the combinations for convertible and sedan respectively.
Number of cars on display = 28/2 = 14 -> decision is to display half the combinations for convertible and sedan respectively.
18 Oct 2023, 02:42
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Excluding Silver, there will be 4 types of exterior colors that are Black, Blue, White and Red and 4 same interior colors. The pairs which is excluded in exterior/interior combinations are Red/Blue or Blue/Red.
For each of the Black and White exterior => 4 possible interior colors are available
For each of the Blue and Red exteriror => 3 possible interior colors are available
Total possible combinations for each type of car => 4+4+3+3=> 14
So total combination of sedan and convertible => 28
Since half of the 14 combinations will be used in convertible and half in sedan, total vehicles to be displayed in auto show => 14
For each of the Black and White exterior => 4 possible interior colors are available
For each of the Blue and Red exteriror => 3 possible interior colors are available
Total possible combinations for each type of car => 4+4+3+3=> 14
So total combination of sedan and convertible => 28
Since half of the 14 combinations will be used in convertible and half in sedan, total vehicles to be displayed in auto show => 14
