Permutation

A permutation is an ordered arrangement of the objects in a collection. They are further classified into two types.

Repetition of Objects: - When a thing has n different types ….. !n

  • Choosing r of something that has n different types, n * ....................... (r time)
  • Example 1: - In the lock, there are 10 numbers to choose from 0-9 and we choose 3 of them, 10 * 10 * 10 = 1000 (n**r)
  • Example 2: - How many 3 digits even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
    • Number of 3 digit even number = 6 * 6 * 3 = 180

Without Repetition of Object: - In this case, we have to reduce the number of available choices each time.

  • Example 3: - In how many ways can a letter of the word PERMUTATIONS be arranged if the: -
    • Words with start with P and ending with S let the first position be P & last position be S (both are fixed) Since letters are repeating.
    • Total number of letters (n) = 10 & since, 2T
    • Vowels are all together,
    • Vowels in word PERMUTATION = (EUAIO)
    • Arranging 5 vowels
    • Total letters in EUAIO = 5
    • Total permutations of 5 letters =
    • There are always 4 letters between P and S?
    • So, there are total 7 cases.
    • But that is when P is before S, there can also be a case where S is before P.
    • Total cases = 7 * 2 = 14 cases
    • Since position of P and S are fixes.
    • Since t is repeating
    • Number of letters = 10
    • 2T’s == 2
    • Number of arrangements
    • Total number of arrangements =
  • Example 4: - How many ways can first and second-placed be awarded to 10 people?

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