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Fundamental Principles of Counting

  1. Principle of Addition : If an event can occur in 'm' ways and another event can occur in 'n' ways independent of the first event, then either of the two events can occur in (m + n) ways.
  2. Principle of Multiplication : If an operation can be performed in 'm' ways and after it has been performed in any one of these ways, a second operation can be performed in 'n' ways, then the two operations in succession can be performed is (m × n) ways.
    nPr and nCr : If 462.png and 'r' is an integer such that 467.png, then we define the following symbols :
    1. P(n, r) or nPr = 472.png
    2. C(n, r) or nCr = 477.png. The symbol nCr is also deonoted by 482.png.

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