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Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC PDF Download

Permutation & Combination

When two tasks are performed in succession, i.e., they are connected by an 'AND', to find the total number of ways of performing the two tasks, you have to MULTIPLY the individual number of ways. When only one of the two tasks is performed, i.e. the tasks are connected by an 'OR', to find the total number of ways of performing the two tasks you have to ADD the individual number of ways.
Example: In a shop there are ‘d’ doors and ‘w’ windows.
Case 1: If a thief wants to enter via a door or window, he can do it in – (d+w) ways.
Case2: If a thief enters via a door and leaves via a window, he can do it in – (d x w) ways.

Linear arrangement of ‘r’ out of 'n' distinct items (nPr): The first item in the line can be selected in 'n' ways AND the second in (n - 1) ways AND the third in (n - 2) ways AND so on. So, the total number of ways of arranging 'r' items out of 'n' is
(n)(n - 1)(n - 2)...(n - r + 1) = Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC

Circular arrangement of 'n' distinct items: Fix the first item and then arrange all the other items linearly with respect to the first item. This can be done in (n - 1)! Ways.

EduRev's Tip: In a necklace, it can be done inImportant Formulae: Permutations & Combinations | CSAT Preparation - UPSC ways.

Selection of r items out of 'n' distinct items (nCr): Arrange of r items out of n = Select r items out of n and then arrange those r items on r linear positions.
Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC

Derangement: If 'n' things are arranged in a row, the number of ways in which they can, be deranged so that none of them occupies its original place is
Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC

EduRev's Tip: Number of ways of arranging 'n' items out of which `p' are alike, 'q' are alike, 'r' are alike in a line is given by = Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC

Partitioning
Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC 

The document Important Formulae: Permutations & Combinations | CSAT Preparation - UPSC is a part of the UPSC Course CSAT Preparation.
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FAQs on Important Formulae: Permutations & Combinations - CSAT Preparation - UPSC

1. What is the formula for permutations?
Ans. The formula for permutations is given by nPr = n! / (n - r)!, where n represents the total number of objects and r represents the number of objects to be selected.
2. What is the formula for combinations?
Ans. The formula for combinations is given by nCr = n! / (r!(n - r)!), where n represents the total number of objects and r represents the number of objects to be selected.
3. How do permutations and combinations differ?
Ans. Permutations and combinations differ in terms of the order of selection. Permutations involve the arrangement of objects in a specific order, while combinations do not consider the order of selection.
4. When should I use permutations?
Ans. Permutations should be used when the order of selection is important. For example, if you need to find the number of ways to arrange a group of people in a line, permutations would be used.
5. When should I use combinations?
Ans. Combinations should be used when the order of selection is not important. For example, if you need to find the number of ways to select a committee from a group of people, combinations would be used.
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