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  • If a certain activity A can be done in “m” different ways and another activity B can be done in “n” different ways, then the total number of ways of doing both A and B simultaneously or sequentially will be m × n.
  • If out of 2 activities, we are doing any one of them, which means either we shall do A or we shall do B, but not both, then the number of ways of doing either A or B will be m + n.
  • The product of first n natural numbers is called factorial n. It is written as n!
  • The number of ways of arranging r objects taken at a time from n objects is called permutations of n objects by taking r objects at a time. Mathematically, we write it as nPr and it is defined as Description: 61070.png
  • Permutations of n things taken all at a time, out of which p things are alike of one kind and q things are alike of another kind is given by Description: 61064.png ways.
  • In circular permutations, if anticlockwise and clockwise order arrangements are considered distinct, then the number of circular permutations of n objects is (n – 1)!.
  • If anticlockwise and clockwise order of arrangements are not distinct, then the number of circular permutations of n things are Description: 61058.png
  • The number of ways of selecting r things from given n things are called combinations of n things by taking r things at a time. It is written as nCr .
    Description: 61052.png 
  • The combinations of selecting r1 objects from a set having n1 objects and r2 objects from a set having n2 objects, where combinations of r1 objects are independent from r2 objects is given by Description: 61045.png

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