1. If one operation can be performed in m ways and another operation in n ways, then the two operations in succesion can be done in m*n ways

 

2. The linear permutation of n distinct objects (that is, the number of ways in which these n objects can be arranged is n! and the circular permutation of n distinct objects is (n-1)! But if the clockwise and anticlockwise directions are indistinguishable then the circular permutations of n different things taken at a time is (n-1)!/2

 

3. But out of these n objects, if there are n1 objects of a certain type, n2 of another type and n3 of another, and so on, Then the number of arrangements (linear permutations) possible is n!/n1!n2!...nz!

 

4. The total number of ways of arranging r things from n things is given by nPr = n!/(n-r)!

 

5. The number of ways to select r things out of n things is given by nCr = n!/(r!*(n-r)!)

 

6. nPr = r! * nCr