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Question

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is

  1. open parentheses table attributes columnalign left columnspacing 1em end attributes row 8 row 4 end table close parentheses minus to the power of 8 P subscript 4
  2. 8 to the power of 4 plus open parentheses table attributes columnalign left columnspacing 1em end attributes row 8 row 4 end table close parentheses
  3. 8 to the power of 4 minus 8 P subscript 4
  4. 8 to the power of 4 minus open parentheses table attributes columnalign left columnspacing 1em end attributes row 8 row 4 end table close parentheses

hintHint:

In the question 8 different letters are given we have to find the number of 4 letter words with at least one letter repeated this means that one letter can be repeated or two letter can be repeated or three or four but no letter repeated is not allowed. So, we will first find the total number 4 letter words formed from 8 letters then we will subtract the number of 4 letter words formed from 8 different letters with no repetition allowed.

The correct answer is: 8 to the power of 4 minus 8 P subscript 4


    Total number of 4 letter words formed from 8 different letters =8 cross times 8 cross times 8 cross times 8 equals 8 to the power of 4
    number of 4 letter words formed from 8 different letters with no repetition allowed =blank to the power of 8 P subscript 4
    So, the number of 4 letter words formed from 8 different letters with at least one letter being repeated =8 to the power of 4 minus blank to the power of 8 P subscript r

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