Question

What 2 things should you remember when answering a question like this? "Two-digit natural numbers are formed, with replacement, from the digits 0 through 9. How many two-digit odd numbers are possible?"

Answer 1

To find the number of possible two-digit odd numbers, consider that there are 9 possible non-zero tens digits and 5 possible odd units digits; the product of these gives 45 possible two-digit odd numbers.

Step-by-step explanation:

When answering the question "How many two-digit odd numbers are possible?", two key points should be remembered:

1. Two-digit numbers must have a non-zero tens digit.
2. An odd number ends with an odd digit (1, 3, 5, 7, or 9).

Now, since the tens digit can be any number from 1 through 9 (to ensure it is a two-digit number), there are 9 possibilities for the first digit. The unit (ones) digit must be odd, and since we are working with the digits 0 through 9, there are 5 possible odd digits (1, 3, 5, 7, 9). The total number of possible two-digit odd numbers can be found by multiplying the number of possibilities for the tens digit by the number of possibilities for the units digit.

So, to calculate this we multiply the 9 possible tens digits by the 5 possible odd unit digits:

9 (tens options) × 5 (odd unit options) = 45 possible two-digit odd numbers.