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How many 4 digit numbers can are there with distinct digits?
4,536 whole numbers or mixed numbers. 5,040 pure decimals.
How many counting numbers have four distinct nonzero digits such that the sum of the four digits is 10?
1,2,3,4 1+2+3+4=10 4 times 3 times 2 times 1 =24 24 counting numbers
How many counting numbers have four distinct nonzero digits that have the sum of the four digits is 11?
1235; 1253; 1325; 1352; 1523; 1532; 2135; 2153; 2315; 2351; 2513; 2531; 3125; 3152; 3215; 3251; 3512; 3521; 5123; 5132; 5213; 5231; 5312; 5321. These are 24 such numbers which have four distinct nonzero digits and add up to 11.
How many three digit numbers have three distinct digits?
For a 3 digit number, the left most or the most significant digit cannot be zero. So it can be 1,2,3,4,5,6,7,8 or 9 which is 9 possibilities. The middle number can be 0,1,2,3,4,5,6,7,8,9 which is 10 possibilties but one of the digits has been chosen already as the first digit, so the possibilities are only 9. The right most number can be 0,1,2,3,4,5,6,7,8,9 which is 10 possibilities but two of the digits have been already used by the left most and the middle digits. That leaves only 8 possibilities. So the total number of three digit numbers that have three distinct digits is 9 x 9 x 8 = 81 x 8 = 648 possibilities
How many strings of 3 decimal digits do not contain the same 3 digits?
How many strings of three digits are there? 000 to 999, or a total of 1000. How many strings of three digits contain the same three digits? That's 000, 111, 222 ... 999! ten in total. The difference is your answer: 1000-10 = 990.
