Permuations And Combinations

Permuations And Combinations

1. Permutations

   • n Dissimilar taken r at a time, nPr=n!/(n-r)!
     • nPr=n.(n-1)P(r-1)
       • nPr=(n-1)Pr+r.(n-1)P(r-1)
   • Sum of all r-digit numbers can be formed using 'n' digits (1<=r<=n<=9)
     • Non-zero
       • (n-1)P(r-1) x sum of given digits 111..1(r times)
     • With zero
       • (n-1)P(r-1) x sum of given digits 111..1(r times)-(n-2)P(r-2) x sum of given digits 111..1(r-1 times)
   • Sets
     • Set A has m elements and the set B has n elements
       • The number of injections from A into B is nPm if m<=n and 0 if m > n
   • Derangements
     • n things in a row , apermutation of these n things such that none of them occupy its original positions is called derangements of n things
       • n!(1/2!-1/3!+1/4!-1/5!+(-1)power n*1/n!)

2. Combination