Published on March 28, 2014
PERMUTATIONS & COMBINATIONS
Introduction Numbers of different arrangements that can be made by taking some or all the items are called permutations of those items. Numbers of different groups that can formed by selecting some or all the items are called combinations of those items
Permutations When these are ‘n’ items and we make arrangements of them taking ‘r’ at a time we get nPr arrangements. nPn means numbers of ‘n’ things taken ‘r’ at a time. Formula : nPr = n( n-1 )( n-2 )…….( n-r+1 ) = n ! _ ( n-r )!
1. Permutations of ‘n’ different things taken ‘r’ at a time Number of arrangements = nPr 2. Permutation where a particular item is to be in a specified place 3. Circular Permutation when there are ‘n’ objects they can be arranged in ( n-1 ) ways. 4. Permutations of things not all different n !_ p! q! r! 5. Permutation with repetition (or replacement) nr
Combinations nCr means the number of combination, without repetition of ‘n’ things taken ‘r’ at a time. Formula: nCr = n !____ r! ( n-r )!
Example 1 : Find who many way a cricket team containing 11 players can be formed from 15 high class players available. Ans: n= 15 and r=11 Number of ways of forming cricket team = 15C11 = 1365
Conclusion Permutation mainly deals with arrangements of a given set of items. And Combination deals with selection of items from a group of items
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