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Permutations and Combinations

  • Factorial notation: The notation n! represents the product of the first n natural numbers, i.e.,
        n! = n × (n − 1) × (n − 2) × …… × 5 × 4 × 3 × 2 × 1
        0! = 1
        
      Example:

 
  • Fundamental Principle of Counting: If an event occurs in m different ways, following which another event occurs in n different ways, then the total number of occurrence of the events in the given order is m × n. This is called the fundamental principle of counting.
      Example:
      Find the number of 5-letter words, with or without meaning, which can be formed out of the letters of the word MATHS,             where the repetition of digits is not allowed.

      Solution:
 …

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