How many positive odd integers less than 10,000 can be represented using the digits 0, 3, 6 an 9?
125
Last digit:0 or 9 (2 choices)
second to fourth digits, 4 choices each.
Total number of four digit odd integers
=4*4*4*2
=128
(these include 9999 and 0009, etc.)
Well, let me calculate that in my clowny way. We have the digits 0, 3, 6, and 9 to work with, which is basically like having a bag of tricks. Now, since we only want positive odd integers, we need to make sure the last digit can only be 3 or 9.
Now, let me pull out my magical clown calculator. We have 10 options for the thousands digit (0-9), 10 options for the hundreds digit, 10 options for the tens digit, and 2 options for the units digit (3 or 9).
So, the total number of positive odd integers less than 10,000 that can be made using the digits 0, 3, 6, and 9 is 10 x 10 x 10 x 2 = 2000. That's a whole circus of possibilities!
To find the number of positive odd integers less than 10,000 that can be represented using the digits 0, 3, 6, and 9, we need to consider the possible arrangements of these digits.
Since we want odd integers, the last digit must be either 3 or 9.
The thousands digit can only be 3, 6, or 9, which gives us 3 choices.
The hundreds digit can be any of the four given digits (0, 3, 6, or 9), giving us 4 choices.
The tens digit can also be any of the four given digits, resulting in 4 choices.
Therefore, the total number of positive odd integers less than 10,000 that can be represented using the digits 0, 3, 6, and 9 is:
3 (thousands digit choices) × 4 (hundreds digit choices) × 4 (tens digit choices) × 2 (choices for the last digit, 3 or 9)
= 3 × 4 × 4 × 2
= 96.
Hence, there are 96 positive odd integers less than 10,000 that can be represented using the digits 0, 3, 6, and 9.
To find the number of positive odd integers less than 10,000 that can be represented using the digits 0, 3, 6, and 9, we can follow these steps:
Step 1: Determine the possible arrangements of the digits.
- Since an odd number must end with either 1, 3, 5, 7, or 9, in this case, our options are limited to 3 and 9.
- The remaining digits (0, 6) can fill the other positions.
Step 2: Count the possible arrangements for each position.
- There are 4 possibilities for the first position (0, 3, 6, 9).
- There are 4 possibilities for the second position.
- There are 4 possibilities for the third position.
- There are 2 possibilities for the last (fourth) position (odd numbers have either 3 or 9 as the last digit).
Step 3: Calculate the total number of arrangements by multiplying the possibilities for each position.
- Total arrangements = 4 x 4 x 4 x 2 = 128
Therefore, there are 128 positive odd integers less than 10,000 that can be represented using the digits 0, 3, 6, and 9.