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  • Need explanation for: The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repitition of digits allowed) is equal to :

The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repitition of digits allowed) is equal to :

  • Option 1)

     

    250

  • Option 2)

     

    374

  • Option 3)

     

    372

  • Option 4)

     

    375

Answers (1)

best_answer

 

Number of Permutations with repetition -

The number of ways of filling r places where each place can be filled by any one of  n objects.

It is n^{r}

- wherein

Where r\geq 0

 

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

3\times 5\times 5\times 5 -1 = 375 - 1 = 374

0000 is not included.


Option 1)

 

250

Option 2)

 

374

Option 3)

 

372

Option 4)

 

375

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