Posted by : Unknown Sunday, 10 July 2016

Permutation is the rearrangement of object or symbols into distinguishable sequences.
Combination is a selection of some or all of a number of different object, it is an un-ordered collection of unique sizes.

Formula:


n, r are non negative integers and r <=n.
r is the size of each permutation.
n is the size of the set from which element are permuted.
! is the factorial operator.

Example 1:
twelve people need to be photographed, but there are only 5 chairs. (The rest of the people will be standing behind and their order does not matter). So how many ways can you sit the twelve people on the 5 chairs?

12x11x10x9x8 = 95040 ways.

Example 2:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

number of ways selecting 3 consonants of 7
= 7C3

number of ways selecting 2 vowels from 4
=4C2

number of ways selecting 3 consonants from 7 and 2 vowels from 4
=    7C3  x 4C2
=(7×6×53×2×1)×(4×32×1)

= (210/6) x (12/2)
=35 x 6
=210

It means you can have 210 group where each groups contains 5 letter (3 consonant and 2 vowels).

number of ways of arranging 5 letter among themselves.
= 5! = 5x4x3x2x1 = 120
Require no of ways = 210 x 120 = 25200



Video:




*Note: if there something you wanna ask just leave a comment, thank you! :D*

{ 5 comments... read them below or Comment }

  1. Hai, how to determine which one is combination and which one is permutation? Thank You :)

    ReplyDelete
    Replies
    1. to determine is that If the order doesn't matter, it is a Combination and, If the order does matter it is a Permutation.

      Delete
  2. This comment has been removed by the author.

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  3. can you answer this question for me? tell me which one is permutation and which one is combination, i think this would help me understand a bit more about which one is permutation and which one is combination, thank you! :).
    a)Selecting three students to attend a conference in Washington, D.C.
    =

    b)Selecting a lead and an understudy for a school play.
    =

    c)Assigning students to their seats on the first day of school.
    =

    ReplyDelete
    Replies
    1. yes i can help you with that, to answer your question just remember, *If the order doesn't matter, it is a Combination and, If the order does matter it is a Permutation.*

      a)Selecting three students to attend a conference in Washington, D.C.
      =Combination.

      b)Selecting a lead and an understudy for a school play.
      =Permutation.

      c)Assigning students to their seats on the first day of school.
      =Permutation.

      Delete

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