Question One. 6 x 5 x 4 x 3 x 2 x 1 = 720.
Question Two. 3 x 5 x 4 x 3 x 2 x 1 = 360
450.
69
36
If you can repeat a digit, there are 27. If you can't repeat a digit, there are only 6.
well the first 9 digit number is 100 million 100,000,000 the last 9 digit number is 999 million 999,999,999 just minus the two numbers and you get... 899,999,999 so there are around 900 million 9 digit numbers.
To find the last but one digit in the product of the first 75 even natural numbers, we need to consider the units digit of each number. Since we are multiplying even numbers, the product will end in 0. Therefore, the last but one digit (tens digit) will depend on the multiplication of the tens digits of the numbers. The tens digit will be determined by the pattern of the tens digits of the even numbers being multiplied.
With 123 digits you can make 123 one-digit numbers.
There are 5460 five digit numbers with a digit sum of 22.
5040 different 4 digit numbers can be formed with the digits 123456789. This is assuming that no digits are repeated with each combination.
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
Excluding numbers which begin with 0, there are 67,200 of them.
27 three digit numbers from the digits 3, 5, 7 including repetitions.
To find the even two-digit numbers where the sum of the digits is 5, we need to consider the possible combinations of digits. The digits that sum up to 5 are (1,4) and (2,3). For the numbers to be even, the units digit must be 4, so the possible numbers are 14 and 34. Therefore, there are 2 even two-digit numbers where the sum of the digits is 5.
Using the digits of 1345678, there are 210 three digit numbers in which no digit is repeated.
There are 900 natural numbers made up of only three digits. This is because there are 9 options for the first digit (1-9), 10 options for the second digit (0-9), and 10 options for the third digit (0-9). Multiplying these options together gives us 9 x 10 x 10 = 900 possible three-digit natural numbers.
There are 238 - 1 = 237 numbers between 1 and 238. To find the number of digits, we need to consider the range of numbers from 1 to 9 (1-digit numbers), 10 to 99 (2-digit numbers), and 100 to 238 (3-digit numbers). There are 9 one-digit numbers, 90 two-digit numbers, and 139 three-digit numbers between 1 and 238, totaling 9 + 90 + 139 = 238 digits.
To find the fraction of 4-digit natural numbers with a product of their digits that is even, we first need to determine the total number of 4-digit natural numbers. There are 9000 such numbers (from 1000 to 9999). Next, we consider the conditions for the product of digits to be even. For a number to have an even product of digits, at least one of the digits must be even. There are 5 even digits (0, 2, 4, 6, 8) and 5 odd digits (1, 3, 5, 7, 9). Therefore, the fraction of 4-digit natural numbers with an even product of digits is 5/10 * 9/10 * 9/10 * 9/10 = 3645/9000 = 809/2000.