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.
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*
Hai, how to determine which one is combination and which one is permutation? Thank You :)
ReplyDeleteto determine is that If the order doesn't matter, it is a Combination and, If the order does matter it is a Permutation.
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ReplyDeletecan 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! :).
ReplyDeletea)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.
=
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.*
Deletea)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.