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
Assuming that the first digit can't be zero: If repetition of digits is permitted: (5 x 6 x 6) = 180 numbers of 3 digits. If repetition of digits is not permitted: (5 x 5 x 4) = 100 numbers of 3 digits.
The number 1234567890 can create about 39 of 40 4 digit numbers.
450.
69
36
With 123 digits you can make 123 one-digit numbers.
There are 5460 five digit numbers with a digit sum of 22.
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.
5040 different 4 digit numbers can be formed with the digits 123456789. This is assuming that no digits are repeated with each combination.
27 three digit numbers from the digits 3, 5, 7 including repetitions.
Using the digits of 1345678, there are 210 three digit numbers in which no digit is repeated.
2893 digits in all, made up as follows: 9 1-digit numbers (1 to 9) = 1*9 = 9 digits 90 2-digit numbers (10 to 99) = 2*90 = 180 digits 900 3-digit numbers (100 to 999) = 3*900 = 270 digit 1 4-digit number (1000) = 4*1 = 4 digits
12689 14689 12489
73 is the largest two-digit number that is prime and has prime numbers for both of its digits.
Any pair of digits (not including 0), can be used to generate 14 four-digit numbers. If one of the digits is 0, only seven will start with a non-zero digit.
7 two-digit numbers.