permuation and combination (SELECTION OF ALIKE AND DIFFRENT / DIVISOR…
permuation and combination
Divisibility test for varius numbers
for 2,4,8,5 set the last position rna and na possible
3,6,9, make all possible cases ra not possible
deal the case of 0 sepratly
DIVISION AND DISTRIBUTION IN GROUPS
TRUE MEANING OF DIVING
division means in how many set of groups of each having a certain number of memeers you can form.just like putting crismas presents in the polythines.
3 formula. :question:
IT MEANS TO DISTRIBUTE THE POLYTHENS IN BETWNNE OBJECT PERMUTATION
this method is further intigrated with fir and ya.
SELECTION OF ALIKE AND DIFFRENT / DIVISOR PROBLEMS
no. of ways to select at least one thing out of n diffrent things
no of ways to select thing from n diffrent things
no. of ways of selecting things from n identical things
no. of ways of selecting at least one thing from n identical things
intagrating with fir and ya to apply them in similar situation
FINDING NUMBER OF DIVISORS
prime factorise the number and express it as a product of prime factors.now select no. of ways of selecting thing fromf n identical thig intigrater fir and ya.
applying condition of the divison such as odd,even,multible of certainn number
SUM OF DIVISORS,GP USE
4 important points of beggar method
none one or more and at least cas
varible eqn problems
used in distribution of identical objects or groups of identical object taken on eat a time using fir and or
SUM BY USING FACE VALUE
first we select then arrang on a circle as the formula of p is not directly applicble on the cicle case.
no. of ways of arranging n thing on a circle i s because 1 point is taken as reference. CLOCKWISE AND ANTICLOCKWISE REFERANCE
GAP METHOD ON CIRCLE
gap and string method both can be applyed on a circle .but is gap method the number of the gaps i sequal to the number of object of use the formula
STRING AND GAP METHOD
used when you do not want certain thing togeter or concusative
1.you let the stuff sit which do not have any condition then you have n+1 gaps then you select gaps and then arrange all the stuff.
you use this method when you want certain things to be always be togeter
in this you take the elements and put them in the bag and treat them as a single element and procide futher keep in mind to arrang the element incide the sack if needed.
problems in which some of the person have problem the use the idential method
SOME INPORTANT RESULTS
FORMULA MULTIMLICATION OF N ODD NUMBERS :!?:
FORMULA TO FIND THE DEGREE :question:
MAXIMISING NCR CONDITION :question:
P AND C BASIC METHODS
it is the number of ways of in which n things can be arrangend takinf p at a time .
it is a two step process
it is the number of ways of selecting n things from m number of things.
tricks and tecnuces of handling ncr.
FUNDEMENTAL PRINCIPAL OF COUNTING
consept of fir
consept of ya
option upon thing consept
basic problems using fumdement principal digit,greter than digit making,just make stagy and apply,answer sheet