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hopefulmba2021
08 Oct 2020, 06:00
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Suppose, I need to select a combination of 2 colours from a catalog of 7 colours. How many different combinations is possible?
1. 7 * 6 =42
Direct Method (FCP approach)
2. 7!/2!5! = 21
Method from Manhattan guide (nCr approach)
Obviously one of them is wrong. Can any expert please explain easily the difference between these 2? And when to use which process?
1. 7 * 6 =42
Direct Method (FCP approach)
2. 7!/2!5! = 21
Method from Manhattan guide (nCr approach)
Obviously one of them is wrong. Can any expert please explain easily the difference between these 2? And when to use which process?
08 Oct 2020, 21:56
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Hi soumyadeeppaul1,
Based on the way your question is worded, we are dealing with a Combination Formula-based prompt. We have 7 colors in total and we have to select a COMBINATION of 2. In these situations, the order of the choices does NOT matter. For example, choosing blue-green is the same as choosing green-blue. In terms of the Combination Formula, that would be:
7!/2!(7-2)! = 7!/2!5! = (7)(6)/(2)(1) = 21 possible combinations.
IF.... the question was altered a bit and instead asked 'with 7 different colors, how many different ways are there to paint a wall if the border of the wall must be a different color from the middle of the wall?' Here, we're clearly dealing with an arrangement (as the color we choose to put on the border will limit the possibilities for the color that we can put in the middle). Here, blue-on-the-border and green-in-the-middle is DIFFERENT from green-on-the-border and blue-in-the-middle. Thus, we have a Permutation:
(7 possible colors for the border)(6 possible remaining colors for the middle) = 42 possible color arrangements.
GMAT assassins aren't born, they're made,
Rich
Based on the way your question is worded, we are dealing with a Combination Formula-based prompt. We have 7 colors in total and we have to select a COMBINATION of 2. In these situations, the order of the choices does NOT matter. For example, choosing blue-green is the same as choosing green-blue. In terms of the Combination Formula, that would be:
7!/2!(7-2)! = 7!/2!5! = (7)(6)/(2)(1) = 21 possible combinations.
IF.... the question was altered a bit and instead asked 'with 7 different colors, how many different ways are there to paint a wall if the border of the wall must be a different color from the middle of the wall?' Here, we're clearly dealing with an arrangement (as the color we choose to put on the border will limit the possibilities for the color that we can put in the middle). Here, blue-on-the-border and green-in-the-middle is DIFFERENT from green-on-the-border and blue-in-the-middle. Thus, we have a Permutation:
(7 possible colors for the border)(6 possible remaining colors for the middle) = 42 possible color arrangements.
GMAT assassins aren't born, they're made,
Rich
hopefulmba2021
GMAT 1: 710 Q48 V37
Posts: 56
08 Oct 2020, 22:18
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Hi Rich,
I understand this concept now based on your explanation.
Also, you just solved my confusion on another thread: https://gmatclub.com/forum/a-firm-has-4 ... s#p2637584
Thanks!
I understand this concept now based on your explanation.
Also, you just solved my confusion on another thread: https://gmatclub.com/forum/a-firm-has-4 ... s#p2637584
Thanks!
