if digits can be repeated, the number of 3 digit odd natural numbers that can be formed using the digits 1, 2, 4, 5, 7 and 9 is
To form a three-digit odd natural number, the units place must be an odd number. Out of the given digits 1, 2, 4, 5, 7, and 9, there are 4 odd digits (1, 5, 7, and 9).
The units place can be filled with these 4 odd digits in 4 ways.
For the first digit (hundreds place), any of the 6 given digits can be used (including 0). So, this place can be filled in 6 ways.
Similarly, for the second digit (tens place), any of the 5 remaining digits can be used. So, this place can be filled in 5 ways.
Overall, the number of 3-digit odd natural numbers that can be formed is 4 * 6 * 5 = 120.
Therefore, the number of 3-digit odd natural numbers that can be formed using the digits 1, 2, 4, 5, 7 and 9 is 120.