Math CentralQuandaries & Queries


Question from Tab:

How many six digit combinations can be made from the numbers zero, two, five, eight? With repetition of numbers

Hi Tab,

You have four digits to work with and six positions to fill so there are

\[4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4^6 \]

ways to produce a six digit string from the four digits, 0, 2, 5 and 8. However some of these strings like $022508$ and $000852$ do not represent six digit numbers since, as numbers, $022508 = 22508$ and $000852 = 852.$ If one of your six digit strings is to represent a six digit number its leftmost digit can't be zero. Hence there are only three choices for the leftmost digit in the string and hence the number of numbers is

\[3 \times 4 \times 4 \times 4 \times 4 \times 4 = 3 \times 4^5\]


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