The number of 5 digit numbers all digits of which are odd is ________.

Step 1 (Identify Candidate Digits): The odd digits are:

There are exactly 5 odd digits.

Step 2 (Apply Choices per Digit Place): We want to construct a 5-digit number where all digits are odd. Let the number be represented by five slots $d_1{d}_2{d}_3{d}_4{d}_5$:

• $d_1$ (ten-thousands place): must be odd (5 choices: 1, 3, 5, 7, 9). Note that since odd digits do not include 0, there is no restriction about starting digit being non-zero.

• $d_2$ (thousands place): 5 choices

• $d_3$ (hundreds place): 5 choices

• $d_4$ (tens place): 5 choices

• $d_5$ (units place): 5 choices

Step 3 (Calculate Total Product): Using the product rule of counting:

Step 4 (Conclusion): There are exactly 3125 such 5-digit numbers.