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How many 7 - digit numbers can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?

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Best answer

To find: number of 7 digit 

0 cannot be in the first place because that would make a 6 digit number 

Total number of 7 - digit numbers = Total number of number possible - Number of numbers with 0 at the first place 

Total number of numbers possible =  \(\frac{7!}{3!2!}\) = 420

Number of numbers with 0 at first place = \(\frac{6!}{3!2!}\) = 60

⇒ Number of 7 - digit numbers = 420 - 60 = 360 

360 seven - digit numbers are possible

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