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Permutation And Combination

 

Permutation and combination important formulas, tricks and shortcuts

Permuation formulas and shortcuts:
Factorial:Let n be a positive integer.Then factorial of n denoted by n! is defined as
n!=1*2*3*……………..(n-2)*(n-1)*n
Note:0!=1
Permutation: Different arrangement of a given number of things by taking some or all at a time.
Example:All arrangements made with letters a,b,c by taking two at a time are ab,ba,bc,cb,ca,ac.
All arrangements made with letters a,b,c by taking all at a time are abc,bca,cab,cba,acb,bac.
Number of permutation:Total number of possible arrangements(permutation) of n things, taken r at a time, is given by:
nPr =n!/(n-r)!=n(n-1)(n-2)………….(n-r+1)
Example 1.Arrangement of 3 items taken 2 at atime
3P2=3!/(3-1)!=3*2=6
Example2. Arrangement of 4 items taken all at a time
4P4=4!/(4-4)!=4!/0!=4*3*2*1=24

Permutation :Important point to note

Combination shortcuts and formulas
 
Each of different groups or selection which can be formed by taking some or all of a number of object, is called a combination.
Suppose we want to select two students from a group of three students namely A,B and C.Then, possible selections are AB,BC and CA.
Note AB and BA represents same selection. But in permutation/arrangement AB and BA represents two different arrangements.
If we want to select ‘all at a time ‘, then there is only one possibility ABC.
Number of combinations:The number of all combination of n things, taken r at a time is:
nCr=n!/((r!)(n-r)!)=[n(n-1)(n-2)….upto r factors]/r!
nCr= nC(n-r)
nCn=1
nC0=1
Example: 10C3=10!/(3!)(10-3)!=(10*9*8)/(1*2*3)=120
 
For solved problems on above formulas please visit below sections: