Math Quiz ( math pigeonhole question)

#1

six different digits are chosen from 1 and 2006…
please explain this

#2

for two numbers to have a difference that is multiple of 5, the numbers must be congruent mod5 (that is, same remainder when divided by 5)
The possible remainders after division by 5 of any number are 0,1,2,3,4
SInce there are 5 options and 6 numbers are chosen, s by pigeonhole principle, the probability is 1