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Presentation On Permutation And Combination

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Published in: Mathematics
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Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

Ajit K / Sharjah

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  1. Permutation & Combination Author/ Email : Ajit Version: VI .0 (26/09/2021)
  2. Definition A combination is a grouping of outcomes in which the order does not matter. A Permutation is a arrangement of outcomes in which the order does matter. Formula The number of combinations of n distinct things chosen r at a time is found using r!(n — r)! Combinations Permutations The number of permutations of n distinct things chosen r at a time is found using np
  3. ImportantFormulae Let n and r be positive integers such that r n, then (ii) n (iii) (iv)
  4. Combination I. Number of ways of selection of r objects out of 'n' distinct objects is Total nutnber of selections out 'n' distinct objects in 2" 2. Method Il : Every element can be dealt in two ways. Either it will be selected or not. So. required ways are 2" 3. The number of selections of r objects out of n identical objects is 1.
  5. Permutation If all objects are distinct : Number of the ways of arranging p elements (all distinct) in a row is p! 2. If some alike objects : Nunlber of ways of arranging p elelnents in a row if out of 'p' objects 'Ill' are alike & 'n' are alike & rest are distict. is given by
  6. Two Specific PnC problems: (a) Gap method (b) Block method
  7. Circular arrangements: Number of ways of arranging n distinct objects in a circle is (n - 1)! If clockwise & anticlockwise arrangements are considered (as in necklace and Garland etc) than number of arrangements are 2
  8. QI. Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is c D 6!
  9. Q . An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is
  10. N/A
  11. __Thank_youX_

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