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Permutation & Combination: Concept of Derangement Video Lecture | Quantitative for GMAT
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FAQs on Permutation & Combination: Concept of Derangement Video Lecture - Quantitative for GMAT
| 1. What is a derangement in permutations and combinations? |  |
Ans.A derangement is a permutation of a set of elements such that none of the elements appear in their original positions. For example, if we have three items labeled A, B, and C, a derangement would be BCA or CAB, as none of the items A, B, or C are in their respective original positions.
| 2. How can we calculate the number of derangements for a set of n elements? | |
Ans.The number of derangements, denoted as !n, can be calculated using the formula:
!n = n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)
This formula is derived from the principle of inclusion-exclusion.
| 3. Can you provide an example of derangements for n = 4? | |
Ans.For n = 4, the elements can be labeled as A, B, C, and D. The derangements for this set include permutations like BADC, CADB, and DCAB, where none of the letters appear in their original positions. The total number of derangements for 4 elements is 9.
| 4. What is the significance of derangements in real-life applications? | |
Ans.Derangements have applications in various fields such as cryptography, error detection, and even in the allocation of tasks where no individual should be assigned to their own task. They help in understanding the randomness and arrangement of items under specific constraints.
| 5. Are there any recursive methods to find derangements? | |
Ans.Yes, derangements can also be calculated using a recursive formula:
!n = (n - 1) * (!(n - 1) + !(n - 2))
This means that the number of derangements of n elements can be derived from the derangements of the previous two numbers.
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