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ten different letters of an alphabet is given. words with five letters are formed from these given letters.then the number of words which have atleast one letter repeatted is69760.prove it?

 ten different letters of an alphabet is given. words with five letters are formed from these given letters.then the number of words which have atleast one letter repeatted is69760.prove it?

Grade:11

3 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear manisha

total number of words of 5 letter from 10 different letter such that any letter can be repeated any number of time = 105

total number of words of 5 letter from 10 different letter such that no letter can be repeated  = 10 *9*8*7*6


now for atleast one letter is repeated = 105 - 10 *9*8*7*6

                                                     =69760

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tatti singh
15 Points
one year ago
5 letters from 1o letters = 5! i.e 120+ 3000 x2 and then multiply it by 10 as there are 10 letters and add 9640
120+60000+9640= 69760.
hope it amazed you. 
 
regards
C ka raja
Kushagra Madhukar
askIITians Faculty 629 Points
11 months ago
Dear student,
Please find the solution to your problem.
 
Total number of words of 5 letter from 10 different letter such that any letter can be repeated any number of time = 105
Total number of words of 5 letter from 10 different letter such that no letter can be repeated  = 10 *9*8*7*6
Now for atleast one letter is repeated = 105  –  10 *9*8*7*6
                                                      = 69760
 
Thanks and regards,
Kushagra

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