Question 890639
For each of the {{{H}}} possible choices for the hundreds digit,
you have {{{T}}} choices for the tens digit,
making {{{H*T}}} choices for the first two digits.
Then for each of those {{{H*T}}} choices,
you have {{{U}}} choices for the last digit,
for a total of
{{{(H*T)*U=H*T*U}}} choices.
 
You cannot use 0 as the first (hundreds) digit, because it would really make a two-digit number.
You have only 3 choices (1, 2, or 3) for the hundreds digit.
The number of possible choices for the hundreds is  {{{H=3}}} .
 
For each of those choices, you have have eliminated one of the digits listed above,
but for the other digits you can also use 0.
As you have 3 digits not yet used that you can use for the tens and units digits,
the number of possible choices for the tens digit is {{{T=3}}} .
 
Each possible choice of hundreds and tens digits leaves you two digits not yet used,
so the number of possible choices for the units digit is {{{U=2}}} .
 
{{{H*T*U=3*3*2=18}}}