5 crucial points to keep in mind while solving a permutation combination problem

1.ARRANGMENT N terms can be arranged in N! ways, if each position can be occupied by one term. N terms can be arranged in NM ways if each position can be occupied by 1 term or 2 terms or …… N terms.  M stands for the number of positions to be filled.

2.COMBINATION M terms can be selected from P terms in [ (P)combination(m) ] ways.

3.In certain situations it is required to first choose the terms and then arrange the terms. i.e.     PERMUTATION.     Permutation = combination x arrangement.

4.When N objects are distributed among P positions such that each position can get any number     of objects (zero, one, two ……N) then the number of ways of arranging the items is [ (N+P-1) combination (P-1) ]

5.When N objects are distributed among P positions such that each position can get atleast one     objet (one, two ……N) then the number of ways of arranging the items is [ (N-1) combination (P+1) ]