4
Simple enough to solve. The answer is a power of two. Assuming you have two possible digits, say for example, 3 and 4, then you simply have to multiply it by how many numbers you want to get the total number of combinations. Each number can be 3 or 4 in this case, and you have 5 numbers. That's two to the fifth. Five combinations of any two numbers. 2x2x2x2x2. The answer is 32 combinations.
Every one of the 5 digits can be either a 5 or a 9 so that means 2 choices for the first, 2 for the second digit, etc. There are 2^5 permutations of the numbers 5 and 9 in a 5 digits number.
There is 1 combination of all ten numbers, 10 combinations of one number and of nine numbers, 45 combinations of two or eight numbers, 120 combinations of three or seven numbers, 210 combinations of four or six numbers and 252 combinations of five numbers. That is 1023 = 210 - 1 in total.
95
45
To determine how many numbers have a sum of digits equal to nine, we consider the possible combinations of digits that add up to nine. These combinations include (9,0), (8,1), (7,2), (6,3), and (5,4). Therefore, there are five possible combinations of digits that sum up to nine.
252 combinations, :)
24680 using only even numbers or 12346 which is an even number
98,764
The answer will depend on how many digits there are in each of the 30 numbers. If the 30 numbers are all 6-digit numbers then the answer is NONE! If the 30 numbers are the first 30 counting numbers then there are 126 combinations of five 1-digit numbers, 1764 combinations of three 1-digit numbers and one 2-digit number, and 1710 combinations of one 1-digit number and two 2-digit numbers. That makes a total of 3600 5-digit combinations.
The number of combinations of five numbers depends on the total number of available numbers to choose from, as well as whether the order of selection matters. If you have a specific set of numbers (for example, 1 to n), you can calculate the combinations using the formula for combinations: ( \binom{n}{r} = \frac{n!}{r!(n-r)!} ), where ( n ) is the total number of numbers and ( r ) is the number of selections (in this case, 5). If no total is specified, the answer cannot be determined.
To find the number of three-digit whole numbers where the sum of the digits equals five, we can represent the three-digit number as (abc), where (a), (b), and (c) are the digits and (a \neq 0) (since (a) is the hundreds place). The equation is (a + b + c = 5). The possible values for (a) (from 1 to 5) lead us to calculate combinations for each case. For each value of (a): (a = 1): (b + c = 4) → (5 combinations: (0,4), (1,3), (2,2), (3,1), (4,0)) (a = 2): (b + c = 3) → (4 combinations: (0,3), (1,2), (2,1), (3,0)) (a = 3): (b + c = 2) → (3 combinations: (0,2), (1,1), (2,0)) (a = 4): (b + c = 1) → (2 combinations: (0,1), (1,0)) (a = 5): (b + c = 0) → (1 combination: (0,0)) Adding these combinations gives a total of (5 + 4 + 3 + 2 + 1 = 15) three-digit whole numbers with the sum of their digits equal to five.