Question 918490
If repetition is not allowed, using the six digits 1, 2, 3, 4, 5, and 7,
we can make {{{6*5*4*3=360}}} sequences of 4 digits.
Each of the six digits used has equal chance of being the first digit,
and since of those digits are less than 4,
half of the 4-digit numbers formed will be less than 4000.
That makes {{{360/2=180}}} 4-digit numbers that are less than 4000.
 
If the number of digits does not matter, using the six digits 1, 2, 3, 4, 5, and 7,
you can make {{{6}}} 1-digit numbers,
{{{6*5=30}}} 2-digit numbers, and
{{{6*5*4=120}}} 3-digit numbers,
for a total of
{{{180+120+30=331}}} numbers that are less than 4000.