3 digit number is a unique number if no digit is repeating A 3 digit number is a unique number if no digit is repeating. In how many ways 3 unique numbers can be chosen such that they do not have any digit in common?

HINT: It doesn’t hurt to see more than one way to do things, so here’s a slightly different approach from the one suggested in the comments. Any set of three different three-digit numbers can be uniquely presented as a list in increasing order. For instance, if you chose the numbers $392,157$, and $684$, the list would be $\langle 157,392,684\rangle$. You want to count the lists of that kind. 
Let $\langle a_1a_2a_3,b_1b_2b_3,c_1c_2c_3\rangle$ be a typical list, where the $a_k,b_k$, and $c_k$ are distinct digits.


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*First choose the increasing list $\langle a_1,b_1,c_1\rangle$ of first digits; in how many ways can you do this? HINT: How many ways are there to pick a set of $3$ distinct first digits? Once you’ve picked them, there’s only one way to list them in increasing order.

*Now choose $a_2,a_3,b_2,b_3,c_2$, and $c_3$ in order; in how many ways can you do that?
