Find how many numbers bigger than 2,999 and less than 8,999 can be formed from the odd digits, if no digits can be repeated.
To find how many numbers can be formed from the odd digits, we need to consider the choices for each position in the number.
First, we need to determine the number of choices for the thousands place. Since the number must be greater than 2,999, the thousands place can only be 3, 5, or 7. So, we have 3 choices for the thousands place.
Next, we need to determine the number of choices for the hundreds place. Any of the five remaining odd digits (1, 3, 5, 7, or 9) can be used for this position. Therefore, we have 5 choices for the hundreds place.
Moving on to the tens place, any of the four remaining odd digits can be used (excluding the digit used for the thousands place and the hundreds place). Thus, we have 4 choices for the tens place.
Finally, for the units place, any of the three remaining odd digits can be used (excluding the digits used for the thousands, hundreds, and tens place). Therefore, we have 3 choices for the units place.
To find the total number of such numbers, we multiply the number of choices for each position:
Total number of numbers = 3 choices for the thousands place × 5 choices for the hundreds place × 4 choices for the tens place × 3 choices for the units place
Total number of numbers = 3 × 5 × 4 × 3
Total number of numbers = 180
Therefore, there can be 180 numbers bigger than 2,999 and less than 8,999 that can be formed from the odd digits if no digits can be repeated.
To find the number of numbers that can be formed from the odd digits, we need to determine the number of choices for each position in the number.
We have to consider three different positions:
1. Thousands place: Since the number must be greater than 2,999, the only option for the thousands place is 3.
2. Hundreds place: We have five odd digits to choose from (1, 3, 5, 7, and 9). However, we have used one odd digit (3) in the thousands place, so we have four options left for the hundreds place.
3. Tens place: Similar to the hundreds place, we have four leftover odd digits to choose from.
Now we can calculate the total number of numbers that can be formed:
Number of choices for thousands place = 1
Number of choices for hundreds place = 4
Number of choices for tens place = 4
Number of choices for units place = 5 (all odd digits)
To find the total number of numbers, we need to multiply the number of choices for each position:
Total = Number of choices for thousands place × Number of choices for hundreds place × Number of choices for tens place × Number of choices for units place
Total = 1 × 4 × 4 × 5
Total = 80
Therefore, there are 80 numbers that can be formed using the odd digits, which are greater than 2,999 and less than 8,999, with no repeated digits.