   SEARCH HOME Math Central Quandaries & Queries  Question from Judy: I need to generate a list of 4 digit numbers using 0-9 where the first digit is 6 and no numbers can be repeated Thank you in advance for your help. Hi Judy,

Since the first digit is a 6 you only need to work with the other three digits. They can be any of the nine digits 0,1,2,3,4,5,7,8,9 with no repeats. Does order matter? For example are 6143 and 6413 different?

If order is not important then the number of items i the list is $\left( \begin{array}{c}9\\3\end{array} \right) = 84.$ You can see a definition of this symbol in a response to an earlier question. if order is important then each of the 84 items in the list can be ordered in 6 ways giving a list with $84 \times 6$ items.

If you want to generate the lists you can use the online Combinations and Permutations Calculator. Set the Types to choose from? to 9, the Number chosen? to be 3, and Is Repetition allowed? to no. In the box labeled List them: put 0,1,2,3,4,5,7,8,9 and then choose List.

Write back if you need more assistance,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.