Permutation Formula and Solved Examples

Permutation

  • In mathematics, permutation is nothing but the combination which is ordered.
  • If we have n objects and out of which we have to arrange r objects where order is considered is given by permutation which has formula,

nPr = n! / (n – r)!

  • Combination is given by, nCr = n! / r! (n – r)!
  • Now, the relation between permutation and combination is given by,

nCr = n! / r! (n – r)! = nPr / r!

 

  • Permutation is used for arranging letters, numbers or data where order of arrangement is considered.

For example:

1.) If the word CHANCE is given, we have to find the number of different ways in which the letters of the word to be arranged.

Ans:

  • In the word CHANCE, there are total 6 letters.
  • But the letter C is repeating two times.
  • Hence, the number of possible different arrangements will be given by,

(Total number of letters)! / (number of repeating letters)!= 6! / 2! = 720/ 2 = 360

  • Thus, we can arrange the letters of the word CHANCE in 360 different ways.

2) If the word is given CHAIR and we have to find the number of possible different ways of arranging letters of that word.

Ans:

  • Here in word CHAIR only 5 different letters are present.
  • Hence the number of different ways of arranging letters of the word CHAIR will be given by,
  • (Total number of different letters)! / (number or repeated letters)! = 5! / 0! = 120/ 1 = 120

Thus, the number of possible different ways of arranging letters of the word CHAIR will be 120.


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