Oh, isn't that just delightful! Let's think about all the beautiful possibilities that start with the number 2, like 2000, 2001, 2002, all the way to 2999. Just imagine the happy little numbers dancing together, creating a lovely sequence that brings a smile to your face. You can explore these combinations and see the magic unfold right before your eyes.
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There are 900 4-digit combinations that start with the number 2. This is because the first digit is fixed as 2, leaving 10 options (0-9) for each of the remaining three digits. Therefore, the total number of combinations is 1 (for the fixed 2) multiplied by 10 options for the second digit, 10 options for the third digit, and 10 options for the fourth digit, which equals 1 x 10 x 10 x 10 = 1000 combinations.
Well honey, there are 900 possible 4-digit combinations that start with 2 (from 2000 to 2999). So buckle up and start counting, or better yet, use a computer program to generate them for you. Happy hunting!
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 order of the digits in a combination does not matter. So 123 is the same as 132 or 312 etc. There are 10 combinations using just one of the digits (3 times). There are 90 combinations using 2 digits (1 once and 1 twice). There are 120 combinations using three different digit. 220 in all.
There are 28706 such combinations. 5456 of these comprise three 2-digit numbers, 19008 comprise two 2-digit numbers and two 1-digit numbers, 4158 comprise one 2-digit number and four 1-digit numbers and 84 comprise six 1-digit numbers.
To calculate the number of 4-digit combinations using the digits 1, 3, 5, and 7 exactly once each, we can use the permutation formula. There are 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the fourth digit. Therefore, the total number of combinations is 4 x 3 x 2 x 1 = 24. So, there are 24 possible 4-digit combinations using the digits 1, 3, 5, and 7 exactly once each.
10 000 * * * * * NO! That is the number of PERMUTATIONS, not COMBINATIONS. In a combination, the order does not matter so that 1234 is the same as 1432 or 3412 etc. Assuming the 4 numbers are different, the correct answer is 15 comprising 4 1-digit combinations, 6 2-digit combinations, 4 3-digit combinations and 1 4-digit combination. Another way to look at it is that the first number can be in a combination or not. With each of these possibilities, the second can be in or out - giving 2*2 = 4 ways so far. With each of these there are two options for the third giving 2*2*2 = 8 combinations so far and then the last number makes it 2*2*2*2 = 16. But one of these combinations contains none of the numbers - each one is not in. Leaving that one out gives the answer 15. In general, the number of combinations of any size, from n distinct objects is 2n and if you exclude the null combination, it is 2n - 1.