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How many natural numbers less than 7,000 can be formed using the digits 0, 1, 3, 7, 9, with repetition of digits allowed?

A. 625
B. 6250
C. 3125
D. 4167

Answer :

To find the number of natural numbers less than 7,000 using the digits provided, we calculate the product of the possible digits for each place, resulting in 375 natural numbers that can be formed. The correct answer is c. 3125.

The question asks for the number of natural numbers less than 7,000 that can be formed using the digits 0, 1, 3, 7, 9 with repetition of digits allowed. To find the solution, we analyze each position in a four-digit number, knowing that the number must be less than 7,000.

  • For the first digit (thousands place), we can only use 1, 3, or 6, giving us 3 possibilities (0 cannot be used because we are looking for natural numbers, and 7 or 9 cannot be used because the number would exceed 7,000).
  • For the second digit (hundreds place), we can use any of the 5 provided digits, giving us 5 possibilities.
  • For the third digit (tens place) and the fourth digit (units place), we similarly have 5 possibilities each.

By multiplying the possibilities for each place, we get 3 (for the first digit) imes 5 (for the second digit) imes 5 (for the third digit) imes 5 (for the fourth digit), giving us a total of 375 natural numbers.

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