Permutation And Combination-1

Permutation And Combination-1 :      

Permutation : The Different arrangements which can be made by taking some or all of the given things or objects at a time is called Permutation.

Eg. All permutations (arrangements) made with the letters a, b, c by taking two at a time will be ab, bc, ca, ba, ac, cb

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Number of Permutations : Number of all permutations of n things, taking r at a time is :



Note : This is valid only when repetition is not allowed.

Rule : Permutation of n different things taken r at a time When repetition is allowed :



Rule : Permutation of n things taking all n things at a time = n!

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Rule : Out of n objects n1 are alike one type, n2 are alike another type, n3 are alike third type, nr are alike another type such that (n1 + n2 + n3 + ......nr)= n

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Combination : Each of the different selections or groups which is made by taking some or all of a number of things or objects at a time is called combination .



Eg. Let we want to select two out of three objects p, q, r, then possible number of selection will be pq, qr, rs

here pq and qp denotes same selection, similarly qr and rq denotes the same selection.

Difference between Permutation and combination :

Let we take three objects a, b, c from this all possible arrangements (Permutations)taking all three at a time will be (abc, acb, bac, bca, cab, cba)

All possible selection taking all three at a time will be only one abc

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Important points :



We can also express it as :

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Ex. In how many ways can the letters of the word PATANA can be arranged ?

Solution : Word PATANA has 6 letters 1P, 3A, 1T, 1N

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Ex. How many words can be formed from the letters of the word " ENGINEERING" , so that vowels always come together ?

Solution : Word ENGINEERING has 11 letters, from which EIEEI are vowels, they can e treated as single letter (EIEEI)NGNRNG,

So seven letters has 3 N, 2 G , 1 R and single (EIEEI)





total number of arrangements = 420 * 10 = 4200 (by rule of multiplication)