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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?

manisha mehra , 14 Years ago
Grade 11
anser 3 Answers
Badiuddin askIITians.ismu Expert

Last Activity: 14 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

Last Activity: 5 Years 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

Last Activity: 4 Years 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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