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Permutation and Combination Tips and Tricks for Government Exams
Theory
Permutation implies an arrangement where the order of things is important and includes word formation, number formation, circular permutation, etc. Combination means selection where order is not important and involves the selection of a team, forming geometrical figures, distribution of things, etc.
Factorial = Factorials are defined for natural numbers, not for negative numbers.
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
Formula
Permutation
- nPr = n! / (n-r)!
- If, from a set of n items, p are of one kind, and q, r are of other kinds respectively, then nPr = n! / (p! × q! × r!).
- nPn = n!
Combination
- nCr = n! / [r! × (n-r)!]
- nC0 = 1
- nCn = 1
- nCr = nCn - r
- nCa = nCb ⇒ a = b ⇒ a+b = n
- nC0 + nC1+ nC2+ nC3+ ...............+ nCn = 2n
Solved Examples
Question for Tips & Tricks: Permutation & CombinationTry yourself:In how many ways the letters of the word ‘MINIMUM’ be arranged taking all the letters? View Solution
Question for Tips & Tricks: Permutation & CombinationTry yourself:In how many ways 5 rings can be worn on 3 fingers? View Solution
Question for Tips & Tricks: Permutation & CombinationTry yourself:In how many ways the letters of the word ‘AUTHOR’ be arranged taking all the letters? View Solution
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FAQs on Tips & Tricks: Permutation & Combination
| 1. What is the difference between permutation and combination? |  |
Ans.Permutation refers to the arrangement of items in a specific order, while combination refers to the selection of items without regard to the order. For example, the arrangements of the letters A, B, and C (ABC, ACB, BAC, etc.) are permutations, whereas selecting any two letters from those three (AB, AC, BC) are combinations.
| 2. How do I calculate the number of permutations of n items taken r at a time? | |
Ans.The number of permutations of n items taken r at a time can be calculated using the formula P(n, r) = n! / (n - r)!, where "!" denotes factorial, which is the product of all positive integers up to that number.
| 3. How do I calculate the number of combinations of n items taken r at a time? | |
Ans.The number of combinations of n items taken r at a time can be calculated using the formula C(n, r) = n! / [r! * (n - r)!], where "!" denotes factorial. This formula accounts for the fact that the order of selection does not matter.
| 4. Can you provide an example of a real-life situation where permutations and combinations are used? | |
Ans.A common real-life example of permutations is arranging books on a shelf. The order in which the books are placed matters, so different arrangements count as different permutations. An example of combinations is selecting team members from a group. The order of selection does not matter; thus, it is a combination.
| 5. What are some common mistakes to avoid when solving permutation and combination problems? | |
Ans.Common mistakes include confusing permutations with combinations (not considering the order), forgetting to apply the factorial function correctly, and failing to account for identical items in a set. To avoid these errors, it's essential to carefully read the problem and identify whether order matters.
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