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Quant05

  1. 1. Chapter 5. Basic Concepts of Permutations and Combinations<br />The factorial n, written as n!, represents the product of all integers from 1 to n both inclusive. <br />Hence, n! = n (n – 1) (n – 2) (n – 3)…. 3.2.1<br />0! = 1<br /> <br />Permutation<br />The ways of arranging or selecting smaller or equal number of persons or objects from a group of persons or collections of objects with due regard being paid to the order of arrangement or selection, are called permutations.<br />Permutations of n things chosen r at a time, nPr = n (n – 1) (n – 2)… (n – r + 1)<br />Revision Notes – Quantitative Aptitude<br />www.cptsuccess.com<br />Page 1 of 1<br />
  2. 2. Chapter 5. Basic Concepts of Permutations and Combinations<br />Properties of Permutation<br />Permutations of n things taken all n things at a time, nPn= n!<br />nPr in factorial notation is written as n! / (n – r)!<br /> <br />Circular Permutation<br />The number of circular permutations of n different things chosen at a time is (n – 1)!<br />The number of ways of arranging n persons along a round table so that no person has the same two neighbors = ½ (n – 1)!<br />The number of necklaces formed with n beads of different colors = = ½ (n – 1)!<br /> <br />Revision Notes – Quantitative Aptitude<br />www.cptsuccess.com<br />Page 1 of 1<br />
  3. 3. Chapter 5. Basic Concepts of Permutations and Combinations<br />Permutations with different conditions applied<br />Number of permutations of n distinct objects when a particular object is not taken in any arrangement is n-1Pr<br />Number of permutations of n distinct objects when a particular object is always included in the arrangement is r. n-1Pr – 1<br /> <br />Combinations<br />The number of ways in which smaller or equal number of things are arranged or selected from a collection of things where the order of selection or arrangement is not important are called combinations<br />Number of combinations of n different things taken r at a time = nCr given that 0 ≤ r ≤ n<br />nCr = n! / r! (n – r)!<br />Revision Notes – Quantitative Aptitude<br />www.cptsuccess.com<br />Page 1 of 1<br />
  4. 4. Chapter 5. Basic Concepts of Permutations and Combinations<br />Properties of nCr<br />nCr = nCn – r (given that 0 ≤ n – r ≤ n)<br />n+1Cr = nCr + nCr-1<br />nC0 = 1<br />nCn = 1<br /> <br />Permutation when some things are alike, all taken at a time<br />P = n! / (p! q! r!) where n is the number of things, p number of the things are exactly of one kind, q of exactly another kind, r of a third kind and the remaining things different.<br />Permutation when each things may be repeated upto r times in an arrangement = nr <br />Revision Notes – Quantitative Aptitude<br />www.cptsuccess.com<br />Page 1 of 1<br />
  5. 5. Chapter 5. Basic Concepts of Permutations and Combinations<br />Combination of n different things taken some or all of n things at a time = 2n – 1<br />Combination of n things taken some or all at a time when p of the things are alike of one kind, q of the things are alike and of another kind and r of the things are alike of a third kind = [(p + 1) (q + 1)(r + 1)….] – 1<br />Combination of selecting r1 things from a set of n1 objects and r2 things from a set of n2 objects where combination of r1 things and r2 things are independent is given by n1Cr1 x n2Cr2<br /> <br />Revision Notes – Quantitative Aptitude<br />www.cptsuccess.com<br />Page 1 of 1<br />

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