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How many natural number are possible by using digits 0,1,3,7,9 (repetition is allowed) which are less than 7000.

How many natural number are possible by using digits 0,1,3,7,9 (repetition is allowed) which are less than 7000.?

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Here, all the five digit number will be greater than 7000, so we choose only 4 digits out of 5 to make the number.

So,

Natural numbers less than 7,000

\underline{1^{st}}, \underline{2^{nd}}, \underline{3^{rd}}, \underline{4^{th}}

There are 3 ways to fill position 1 (i.e. 0,1,3) because a 4 digit number starting from 7 and 9 would be greater than 7000. 

and for the remaining position, there are 5 ways each so,

3\times 5\times 5\times 5 -1 = 375

As 0000 is not included,

Number of Natural numbers less than 7,000 = 375 - 1 = 374.

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