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Permutation & Combination: Concept of Derangement for CAT Video Lecture | Quantitative for GMAT
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FAQs on Permutation & Combination: Concept of Derangement for CAT Video Lecture - Quantitative for GMAT
| 1. What is the concept of derangement in permutation and combination? |  |
Ans. Derangement is a concept in permutation and combination that deals with arranging objects in such a way that none of them occupy their original positions. In other words, it is a permutation where no element appears in its original position.
| 2. How is derangement different from a regular permutation? | |
Ans. In a regular permutation, all elements can be arranged in any position, including their original position. However, in derangement, no element can appear in its original position. This restriction makes derangement a bit more challenging and interesting.
| 3. How do we calculate the number of derangements? | |
Ans. The number of derangements of n objects can be calculated using the formula:
D(n) = n!(1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)
Here, n! represents the factorial of n, and (-1)^n represents the alternating sign.
| 4. Can derangement be applied to real-life situations? | |
Ans. Yes, the concept of derangement can be applied to real-life situations. For example, if you have a group of friends and you want to assign each person a Secret Santa without anyone getting their own name, you can use derangement to calculate the number of possible assignments.
| 5. How can the concept of derangement be useful in probability problems? | |
Ans. Derangement can be used in probability problems that involve arranging objects or events in a way that none of them occur in their original order. It helps in calculating the probability of such events occurring and provides a different perspective on permutation and combination problems.
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