Quandaries and Queries



There are four close friends having a heated discussion concerning the the number of three digit combinations using the numbers 0 through 9. The discussion involves the daily lottery.  Any assistance you can lend would be greatly appreciated.




Hi Fred,

In the lottery I expect that three digits are selected at random from the ten digits 0,1,2...,9 so that no digit can be repeated. You can count the number of possibilities if you think about the process that is uses to select the three winning digits.

For the first digit selected there are ten possibilities. Once you have selected the first digit, there are nine possibilities for the second digit. Thus there are 109=90 possibilities if you are selecting two digits. Regardless of what two digits you have selected at this moment, there are eight possibilities for the third digit. Hence, in total there are 1098=720 possible combinations.



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