There are 10!/(4!(10-4)!) = 210 such combinations assuming no repeats are allowed:
{0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 2, 5}, {0, 1, 2, 6}, {0, 1, 2, 7}, {0, 1, 2, 8}, {0, 1, 2, 9}, {0, 1, 3, 4}, {0, 1, 3, 5},
{0, 1, 3, 6}, {0, 1, 3, 7}, {0, 1, 3, 8}, {0, 1, 3, 9}, {0, 1, 4, 5}, {0, 1, 4, 6}, {0, 1, 4, 7}, {0, 1, 4, 8}, {0, 1, 4, 9},
{0, 1, 5, 6}, {0, 1, 5, 7}, {0, 1, 5, 8}, {0, 1, 5, 9}, {0, 1, 6, 7}, {0, 1, 6, 8}, {0, 1, 6, 9}, {0, 1, 7, 8}, {0, 1, 7, 9},
{0, 1, 8, 9}, {0, 2, 3, 4}, {0, 2, 3, 5}, {0, 2, 3, 6}, {0, 2, 3, 7}, {0, 2, 3, 8}, {0, 2, 3, 9}, {0, 2, 4, 5}, {0, 2, 4, 6},
{0, 2, 4, 7}, {0, 2, 4, 8}, {0, 2, 4, 9}, {0, 2, 5, 6}, {0, 2, 5, 7}, {0, 2, 5, 8}, {0, 2, 5, 9}, {0, 2, 6, 7}, {0, 2, 6, 8},
{0, 2, 6, 9}, {0, 2, 7, 8}, {0, 2, 7, 9}, {0, 2, 8, 9}, {0, 3, 4, 5}, {0, 3, 4, 6}, {0, 3, 4, 7}, {0, 3, 4, 8}, {0, 3, 4, 9},
{0, 3, 5, 6}, {0, 3, 5, 7}, {0, 3, 5, 8}, {0, 3, 5, 9}, {0, 3, 6, 7}, {0, 3, 6, 8}, {0, 3, 6, 9}, {0, 3, 7, 8}, {0, 3, 7, 9},
{0, 3, 8, 9}, {0, 4, 5, 6}, {0, 4, 5, 7}, {0, 4, 5, 8}, {0, 4, 5, 9}, {0, 4, 6, 7}, {0, 4, 6, 8}, {0, 4, 6, 9}, {0, 4, 7, 8},
{0, 4, 7, 9}, {0, 4, 8, 9}, {0, 5, 6, 7}, {0, 5, 6, 8}, {0, 5, 6, 9}, {0, 5, 7, 8}, {0, 5, 7, 9}, {0, 5, 8, 9}, {0, 6, 7, 8},
{0, 6, 7, 9}, {0, 6, 8, 9}, {0, 7, 8, 9}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 3, 7}, {1, 2, 3, 8}, {1, 2, 3, 9},
{1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 4, 7}, {1, 2, 4, 8}, {1, 2, 4, 9}, {1, 2, 5, 6}, {1, 2, 5, 7}, {1, 2, 5, 8}, {1, 2, 5, 9},
{1,2, 6, 7}, {1, 2, 6, 8}, {1, 2, 6, 9}, {1, 2, 7, 8}, {1, 2, 7, 9}, {1, 2, 8, 9}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 4, 7},
{1, 3, 4, 8}, {1, 3, 4, 9}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 3, 5, 8}, {1, 3, 5, 9}, {1, 3, 6, 7}, {1, 3, 6, 8}, {1, 3, 6, 9},
{1, 3, 7, 8}, {1, 3, 7, 9}, {1, 3, 8, 9}, {1, 4, 5, 6}, {1, 4, 5, 7}, {1, 4, 5, 8}, {1, 4, 5, 9}, {1, 4, 6, 7}, {1, 4, 6, 8},
{1, 4, 6, 9}, {1, 4, 7, 8}, {1, 4, 7, 9}, {1, 4, 8, 9}, {1, 5, 6, 7}, {1, 5, 6, 8}, {1, 5, 6, 9}, {1, 5, 7, 8}, {1, 5, 7, 9},
{1, 5, 8, 9}, {1, 6, 7, 8}, {1, 6, 7, 9}, {1, 6, 8, 9}, {1, 7, 8, 9}, {2, 3, 4, 5}, {2, 3, 4, 6}, {2, 3, 4, 7}, {2, 3, 4, 8},
{2, 3, 4, 9}, {2, 3, 5, 6}, {2, 3, 5, 7}, {2, 3, 5, 8}, {2, 3, 5, 9}, {2, 3, 6, 7}, {2, 3, 6, 8}, {2, 3, 6, 9}, {2, 3, 7, 8},
{2, 3, 7, 9}, {2, 3, 8, 9}, {2, 4, 5, 6}, {2, 4, 5, 7}, {2, 4, 5, 8}, {2, 4, 5, 9}, {2, 4, 6, 7}, {2, 4, 6, 8}, {2, 4, 6, 9},
{2, 4, 7, 8}, {2, 4, 7, 9}, {2, 4, 8, 9}, {2, 5, 6, 7}, {2, 5, 6, 8}, {2, 5, 6, 9}, {2, 5, 7, 8}, {2, 5, 7, 9}, {2, 5, 8, 9},
{2, 6, 7, 8}, {2, 6, 7, 9}, {2, 6, 8, 9}, {2, 7, 8, 9}, {3, 4, 5, 6}, {3, 4, 5, 7}, {3, 4, 5, 8}, {3, 4, 5, 9}, {3, 4, 6, 7},
{3, 4, 6, 8}, {3, 4, 6, 9}, {3, 4, 7, 8}, {3, 4, 7, 9}, {3, 4, 8, 9}, {3, 5, 6, 7}, {3, 5, 6, 8}, {3, 5, 6, 9}, {3, 5, 7, 8},
{3, 5, 7, 9}, {3, 5, 8, 9}, {3, 6, 7, 8}, {3, 6, 7, 9}, {3, 6, 8, 9}, {3, 7, 8, 9}, {4, 5, 6, 7}, {4, 5, 6, 8}, {4, 5, 6, 9},
{4, 5, 7, 8}, {4, 5, 7, 9}, {4, 5, 8, 9}, {4, 6, 7, 8}, {4, 6, 7, 9}, {4, 6, 8, 9}, {4, 7, 8, 9}, {5, 6, 7, 8}, {5, 6, 7, 9},
{5, 6, 8, 9}, {5, 7, 8, 9}, {6, 7, 8, 9}
If repeats are allowed, the number increases to 715 combinations - I'll leave it as an exercise for the reader to list the extra 505 combinations.
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There are a total of 10 options for each digit in a 4-digit combination, as there are 10 numbers (0-9) to choose from. Therefore, the total number of possible combinations is calculated by multiplying the number of options for each digit (10) by itself four times, which is 10^4. This equals 10,000 possible 4-digit combinations using the numbers 0 through 9.
Oh, what a happy little question! There are 10 choices for each digit in a 4-digit combination, ranging from 0 to 9. So, the total number of combinations is simply 10 x 10 x 10 x 10, which equals 10,000 possibilities. Isn't that just delightful? Just imagine all the beautiful combinations waiting to be discovered!
Oh honey, there are 10 choices for each digit, so that's 10 x 10 x 10 x 10, which equals 10,000 possible 4-digit combinations. So, buckle up and start memorizing those numbers if you want to crack any codes or impress your friends with your math skills.
To calculate the number of different 4-digit combinations that can be made using numbers 0 through 9, we use the concept of permutations. Since repetition is allowed, we use the formula for permutations with repetition, which is n^r, where n is the number of options for each digit (10 in this case) and r is the number of digits (4 in this case). Therefore, the number of different 4-digit combinations that can be made using numbers 0 through 9 is 10^4, which equals 10,000 combinations.
In other words, how many 4 digit combination locks are there using the digits 0-9 on each wheel. There are 10×10×10×10 = 10⁴ = 10,000 such combinations.
There are 10,000 possible combinations, if each number can be used more than once.
There are 9C3 = 84 combinations.
There are 210 4 digit combinations and 5040 different 4 digit codes.