Combinations and Permutations Combinations and Permutations


Combinations and PermutationsCombinations and Permutations

Permutation and combination related questions are common in PSC and Bank exams.

Before going to Combinations and Permutations, first lean about factorial.

If \'n\' is a positive integer then, factorial of n is denoted as n!.


5! = ( 1 x 2 x 3 x 4 x 5 ) = 120

4! = (1 x 2 x 3 x 4 ) = 24


Permutations are for lists of items, whose order matters and combinations are for group of items where order doesn’t matter. in other words,

  • When the order of items doesn\'t matter, it is called as Combination.
  • When the order of items does matter it is called as Permutation.


The number of permutations of n objects taken r at a time is determined by using this formula:

P(n,r)=n!/(n−r)!

Permutation: Listing your 3 favourite football team in order, from list of 10 teams. P(10,3) = 720.


The number of combinations of n objects taken r at a time is determined by using this formula:

C(n,r)=n!/((n−r)!r!)

Combination: Picking a team of 3 people from a football coaching group of 10. C(10,3) = 10!(3!(10−3)!) = 120.

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Average calculation

N = the number of terms  .

S = the sum of the numbers in the set.

Average = S/N .


For example.

The marks of a student in five subjects are 96, 94, 92, 87, and 81, then what is the average score of the student?.

N = 5.

S = 96 + 94 + 92 + 87 + 81 = 450.

A = 450/5 = 90.


Another type questions .

1). There are 36 boys and 44 girls in a class. The average score of boys is 40 and girls are 35. Then what will be the average mark? .


Total mark of 36 boys = 36 x 40 = 1440.

Total mark of 44 girls = 35 x 44 = 1540.

Total mark of 80 Students = 1440 + 1540 = 2980 .

Average mark of the class = (2980 / 80).

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അടിയന്തരാവസ്ഥ   : ജർമനി.

കണ്‍കറന്റു ലിസ്റ്റ്   : ആസ്ത്രേലിയ.

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പാർലമേന്റരി ജനാധിപത്വം : ബ്രിട്ടണ്‍.

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മൌലിക അവകാശങ്ങൾ : യു എസ് എ.

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