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Permutation and combination
Permutation and combination is one of topics which students find it difficult to crack but understanding of certain terms fully can surely help in cracking those things in easy way.
Permutation and combination in GMAT does not include many formulas . it is just 2-3 formulas and their application which can sum the entire thing
nPr = n!/(n-r)! permutation
the above formula refers to distribution or arrangement of r places for n people or vice versa.i..e distribution of n people at r places.
example :
3 toys need to be distributed to 2 people
using formula we get : 3!/1!=6
if we make cases
each toy can go to any of 2 people
so total cases for 3 toys =3*2=6 toys
nCr=n!/r!(n-r)! combination
Unlike permutation , this formula usage is bit different. It means selecting n things out of r things
example : we need to select 2 people out of 5 people for training
using formula : 5C2=5!/2!3!=10
Making cases for ABCDE
AB,AC,AD,AE,BC,BD,BE,CD,CE,DE
total cases=10
Counting principle
Putting dashes and filling out numbers
example :calculate total no of two digit numbers
_ _
1st dash can be filled in 9 ways (all except zero) , 2nd dash can be filled in 10 ways
total cases : 9*10=90
making cases : highest =99 Smallest=10
total cases =99-10+1=90
These formulas/techniques make our life easier otherwise we need to calculate whole bunch of valid cases to arrive at answer.
Give kudos if it helps
Permutation and combination is one of topics which students find it difficult to crack but understanding of certain terms fully can surely help in cracking those things in easy way.
Permutation and combination in GMAT does not include many formulas . it is just 2-3 formulas and their application which can sum the entire thing
nPr = n!/(n-r)! permutation
the above formula refers to distribution or arrangement of r places for n people or vice versa.i..e distribution of n people at r places.
example :
3 toys need to be distributed to 2 people
using formula we get : 3!/1!=6
if we make cases
each toy can go to any of 2 people
so total cases for 3 toys =3*2=6 toys
nCr=n!/r!(n-r)! combination
Unlike permutation , this formula usage is bit different. It means selecting n things out of r things
example : we need to select 2 people out of 5 people for training
using formula : 5C2=5!/2!3!=10
Making cases for ABCDE
AB,AC,AD,AE,BC,BD,BE,CD,CE,DE
total cases=10
Counting principle
Putting dashes and filling out numbers
example :calculate total no of two digit numbers
_ _
1st dash can be filled in 9 ways (all except zero) , 2nd dash can be filled in 10 ways
total cases : 9*10=90
making cases : highest =99 Smallest=10
total cases =99-10+1=90
These formulas/techniques make our life easier otherwise we need to calculate whole bunch of valid cases to arrive at answer.
Give kudos if it helps
Archived Topic
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