What do we mean by Permutation and Combination in mathematics? (Brief explanation)
Discuss ko muna ulit yung Factorial Notation (galit na number hahaha)
Let n be a positive integer. Then, factorial n, denoted n! is defined as:
n! = n(n - 1)(n - 2) ... 3.2.1.
Examples:
We define 0! = 1.
4! = (4 x 3 x 2 x 1) = 24.
5! = (5 x 4 x 3 x 2 x 1) = 120.
Kuha na? Gagamitin kasi natin yan factorial na yan sa permutation at combination
Permutations:
The different arrangements of a given number of things by taking some or all at a time, are called permutations.(mahalaga yung order dito or pagkasunod sunod)
Examples:
All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb).
All permutations made with the letters a, b, c taking all at a time are:
( abc, acb, bac, bca, cab, cba)
Number of Permutations:
Number of all permutations of n things, taken r at a time, is given by:
nPr = n(n - 1)(n - 2) ... (n - r + 1) =
n!/(n - r)!
Examples:
6P2 = 6!/(6-2)! = 6!/4! = (6x5x4!)/4! =30
Kuha na? Isa pa.
7P3 = 7!/(7-3)! = 7!/4! = 210
Cor. number of all permutations of n things, taken all at a time = n!.
An Important Result:
If there are n subjects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind,
such that (p1 + p2 + ... pr) = n.
Then, number of permutations of these n objects is =
n!/(p1!).(p2)!.....(pr!) gets na?
Example ulit, eto yung sa letter,
How many arrangement can ba made in the word MATHEMATICS?
●ilan yung letter? 11 diba? So 11!
●may parehas bang letter? Oo dalawa yung T, A, at M
So 11!/2!2!2! Ang gagawin.
Combinations:
Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination. (Kahit sino mauna, ayub yung pinagkaiba niya sa permutation)
Examples:
Suppose we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA.
Note: AB and BA represent the same selection.
All the combinations formed by a, b, c taking ab, bc, ca.
The only combination that can be formed of three letters a, b, c taken all at a time is abc.
Various groups of 2 out of four persons A, B, C, D are:
AB, AC, AD, BC, BD, CD.
Note that ab ba are two different permutations but they represent the same combination.
Formula of combination:
n!/r!(n-r)! Mapapansin nyo na may nadagdag na r! .
Yan lang muna: :) hope you learn <3
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-luyde
