Page 1 CPT Section D Quantitative Aptitude Chapter 5 Preethi Rathi Page 2 CPT Section D Quantitative Aptitude Chapter 5 Preethi Rathi Selecting smaller or equal number of persons or objects and the importance is given to the arrangement or order in which the objects are placed is called permutations. Therefore out of â€˜nâ€™ things if â€˜râ€™ things are arranged then the number of arrangements is called as permutations. np r = n!/(n-r)! =n(n-1)(n-2)â€¦(n-r+1) 5p 3 =5!/(5-3)!=5x4x3=60 Page 3 CPT Section D Quantitative Aptitude Chapter 5 Preethi Rathi Selecting smaller or equal number of persons or objects and the importance is given to the arrangement or order in which the objects are placed is called permutations. Therefore out of â€˜nâ€™ things if â€˜râ€™ things are arranged then the number of arrangements is called as permutations. np r = n!/(n-r)! =n(n-1)(n-2)â€¦(n-r+1) 5p 3 =5!/(5-3)!=5x4x3=60 1. np r + r.np r-1 = n+1p r 2. Sum of all â€˜râ€™ digits numbers [1 to 9], excluding 0 is n-1p r-1 x(sum of digits) x 111â€¦..r times. 3. Sum of all â€˜râ€™ digit numbers including â€˜0â€™ is 4. Sum [n-1pr-1 x 111â€¦..r times â€“ n-2pr-2 x 111â€¦(r-1)times] Page 4 CPT Section D Quantitative Aptitude Chapter 5 Preethi Rathi Selecting smaller or equal number of persons or objects and the importance is given to the arrangement or order in which the objects are placed is called permutations. Therefore out of â€˜nâ€™ things if â€˜râ€™ things are arranged then the number of arrangements is called as permutations. np r = n!/(n-r)! =n(n-1)(n-2)â€¦(n-r+1) 5p 3 =5!/(5-3)!=5x4x3=60 1. np r + r.np r-1 = n+1p r 2. Sum of all â€˜râ€™ digits numbers [1 to 9], excluding 0 is n-1p r-1 x(sum of digits) x 111â€¦..r times. 3. Sum of all â€˜râ€™ digit numbers including â€˜0â€™ is 4. Sum [n-1pr-1 x 111â€¦..r times â€“ n-2pr-2 x 111â€¦(r-1)times] np n = n! np 1 = n np 0 = 1 0! = 1 np r = n.(n-1)p(r-1) Page 5 CPT Section D Quantitative Aptitude Chapter 5 Preethi Rathi Selecting smaller or equal number of persons or objects and the importance is given to the arrangement or order in which the objects are placed is called permutations. Therefore out of â€˜nâ€™ things if â€˜râ€™ things are arranged then the number of arrangements is called as permutations. np r = n!/(n-r)! =n(n-1)(n-2)â€¦(n-r+1) 5p 3 =5!/(5-3)!=5x4x3=60 1. np r + r.np r-1 = n+1p r 2. Sum of all â€˜râ€™ digits numbers [1 to 9], excluding 0 is n-1p r-1 x(sum of digits) x 111â€¦..r times. 3. Sum of all â€˜râ€™ digit numbers including â€˜0â€™ is 4. Sum [n-1pr-1 x 111â€¦..r times â€“ n-2pr-2 x 111â€¦(r-1)times] np n = n! np 1 = n np 0 = 1 0! = 1 np r = n.(n-1)p(r-1) Divisibility by 2: A numeric number is divisible by 2 if the last digit i.e., the digits in the units place is either even or zero. Divisibility by 3: A number is divisible by 3 if the sum of the digits is multiple of 3Read More

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