how many 7 digit numbers can be formed using digits 1,2,0,2,4,2,4

with repetion of digits 

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since you have seven blanks to fill therefore in the first blank we have 6 chocies to fill as we cant use 0 or the number will be 6 digits . so we have filled the first blank with suppose any number say 1 

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now since repetition is allowed . therefore for second blank we have 7 choices . similarly we have 7 choices for all other blanks . 

 

so no of ways would be 6*7*7*7*7*7*7

which is 705,894

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now if repetition is not alowed:

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we have same blanks in first one . same as above we have 6 choices. lets fill it with say 2 

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now as we have used 2 once so we cannot use this same 2 again. now for the second blank since 2 is used and we can use 0 as well so we have same 6 chocies . lets fill it with a number say 0.

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now procedding similar as above we have 5 chocies for 3^rd balnk and 4 choices for 4^th blank and 3 chocies for 5^th blank and 2 choices for 6^th blank and 1 choice for last blank .

 

so in total we have 6*6*5*4*3*2*1 chocies  which is equal to 4,320

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so when repetition is allowed we have 705,894 choices and when repetition is not allowed we have 4,320 chocies . 

 

Hope I Helped, 

Have a nice day.