998,000
There are 5 numbers which can make the 3 digit numbers in this example. Therefore each digit in the 3 digit number has 5 choices of which number can be placed there. Therefore number of 3 digit numbers = 5 x 5 x 5 = 125
Multiplying by multi-digit numbers is similar to multiplying by two-digit numbers in that both processes involve breaking down the numbers into place values and multiplying each digit by each digit in the other number. The key similarity lies in the application of the distributive property, where each digit in one number is multiplied by each digit in the other number, and then the products are added together to get the final result. This process is consistent whether you are multiplying by a two-digit number or a multi-digit number.
4 options for the first digit, 3 options for the second digit, 2 options for the third digit. Multiply the number of options together, and you find how many 3-digit numbers you can get.
For each number, there are four digits, and for each digit, there are two possibilities for digits: 3 or 4. So the number of 4-digit numbers is 2*2*2*2 = 16. The 4-digit numbers using 3 and 4 are: 3333 3334 3343 3344 3433 3434 3443 3444 4333 4334 4343 4344 4433 4434 4443 4444
998,000
There are 5 numbers which can make the 3 digit numbers in this example. Therefore each digit in the 3 digit number has 5 choices of which number can be placed there. Therefore number of 3 digit numbers = 5 x 5 x 5 = 125
Multiplying by multi-digit numbers is similar to multiplying by two-digit numbers in that both processes involve breaking down the numbers into place values and multiplying each digit by each digit in the other number. The key similarity lies in the application of the distributive property, where each digit in one number is multiplied by each digit in the other number, and then the products are added together to get the final result. This process is consistent whether you are multiplying by a two-digit number or a multi-digit number.
There are four of each.
When creating a 3-digit number using the digits 3, 6, and 9, with repetition allowed, each digit has 3 possible choices. Therefore, the total number of 3-digit numbers that can be formed is calculated by multiplying the number of choices for each digit, which is 3x3x3 = 27. So, there are 27 different 3-digit numbers that can be made using the digits 3, 6, and 9 with repetition allowed.
4 options for the first digit, 3 options for the second digit, 2 options for the third digit. Multiply the number of options together, and you find how many 3-digit numbers you can get.
24 = 4*3*2*1 of them
61
For each number, there are four digits, and for each digit, there are two possibilities for digits: 3 or 4. So the number of 4-digit numbers is 2*2*2*2 = 16. The 4-digit numbers using 3 and 4 are: 3333 3334 3343 3344 3433 3434 3443 3444 4333 4334 4343 4344 4433 4434 4443 4444
the place of each digit help the value of the number by using your multuplication
6*5*4*3=360
To find the total number of seven-digit numbers that contain the number seven at least once, we can use the principle of complementary counting. There are a total of 9,999,999 seven-digit numbers in total. To find the number of seven-digit numbers that do not contain the number seven, we can count the number of choices for each digit (excluding seven), which is 9 choices for each digit. Therefore, there are 9^7 seven-digit numbers that do not contain the number seven. Subtracting this from the total number of seven-digit numbers gives us the number of seven-digit numbers that contain the number seven at least once.