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
the first digit must be 3,5,7
the other digits can be 1,3,5,7,9
since the 1st digit cannot be repeated, that means the last 3 digits must be formed using only 4 of the available choices, giving
4*3*2 choices.
So, since the 1st digit can be chosen 3 ways, there are
3*4*3*2 ways to pick the digits.
72
To find the number of numbers that can be formed from the odd digits between 2,999 and 8,999 without repetition, we need to consider each position in the number.
First, we determine the number of choices for the thousands digit. Since it must be greater than 2, we can choose from the digits 3, 5, 7, and 9. So, there are 4 choices for the thousands digit.
For the hundreds digit, we can use any of the odd digits from 0 to 9, excluding the digit used for the thousands digit. So, there are 5 choices for the hundreds digit.
Similarly, for the tens and units digits, we have 5 choices for each, again excluding the digits already used in the thousands and hundreds places.
Therefore, the total number of numbers that can be formed is:
4 (choices for the thousands digit) × 5 (choices for the hundreds digit) × 5 (choices for the tens digit) × 5 (choices for the units digit) = 500 numbers
To find how many numbers can be formed from the odd digits, we need to determine the number of choices we have for each digit position.
First, let's consider the thousands place. Since the number must be greater than 2,999, the only choice for this position is 3.
Next, let's consider the hundreds place. The available odd digits to choose from are 1, 3, 5, 7, and 9. However, the number must be less than 8,999. So the choices for this position depend on the digit chosen for the thousands place (which is 3). If the thousands place is 3, then the hundreds place can be any of the five odd digits, including 1, 5, 7, and 9. So we have 4 choices for this position.
Now let's consider the tens place and units place together. Again, the available odd digits to choose from are 1, 3, 5, 7, and 9. However, the number must be less than 8,999, so the choices for these two positions depend on the digits chosen for the thousands and hundreds places. If the thousands place is 3 and the hundreds place is any of the four odd digits, then the tens and units place can be any of the five odd digits, including 1, 3, 5, 7, and 9. So we have a total of 5 choices for these two positions.
Now we can calculate the total number of possible numbers:
1 choice for the thousands place, multiplied by 4 choices for the hundreds place, multiplied by 5 choices for the tens and units place, gives us a total of 1 * 4 * 5 = 20.
Therefore, there are 20 numbers that can be formed from the odd digits, which are greater than 2,999 and less than 8,999, with no digit repeated.