You can make 27 unique three-digit numbers using the three digits 0, 1, and 2.
i.e. for each of the three digits abc, there are 9 possible orders of those, from aaa to ccc.
The 9 starting with 0:
000
001
002
010
011
012
020
021
022
* the combinations are the same as the numbers 0 to 26 expressed in base 3 (000 to 222)
26 base 3 = 222 = 18 + 6 + 2 = 26
If the numbers are not repeated then the highest 5 digit even number to be made out of 0123456789 is : 98764.
This is easy. Just sort the digits in descending order. That works because the further left you go, the more significant the digit. So the largest number that can be made out of the digits 5, 3, 1, 4, and 7 is 75,431.
prime numbers
Prime numbers cannot be made up from multiplying other numbers. Primary colours cannot be made up from adding other colours.
Introduction of the digit 0 as a place holder.
-4
1
6*7*7 = 294
24 three digit numbers if repetition of digits is not allowed. 4P3 = 24.If repetition of digits is allowed then we have:For 3 repetitions, 4 three digit numbers.For 2 repetitions, 36 three digit numbers.So we have a total of 64 three digit numbers if repetition of digits is allowed.
6 ways: 931,913,139,193,391,319
999
10
999-111=888 888 3 digit numbers can be made with numbers between 1 - 9
It is a permutation problem (any number can be used repeatedly), it will become 4 x 4 x 4 x 4 = 256 four digit numbers. If each number can only be used once, then the answer is 4 x 3 x 2 x 1 = 24 four digit numbers.
If this is a homework assignment, please consider trying it yourself first, otherwise the value of the reinforcement to the lesson offered by the homework will be lost on you.There are 60 possibilities that can be made for a three digit number using the numbers 2 4 6 8 and 9. (5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit - multiply 5, 4, and 3, and you get 60.)To determine how many of these three digit numbers are smaller than 500, consider that, given 2 4 6 8 and 9, the first digit would have to be 2 or 4. That gives 2 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit. Multiply 2, 4, and 3, and you get 24.
You can select 12 numbers for the first digit, 11 numbers for the second digit, and 10 numbers for the third digit; so 12*11*10 = 1320 sets of 3 numbers can be made out of 12 different numbers.
There are 12 such numbers.