What is the wrong with your instructor`s answer ?
1st digit - 1,2,3,4,5,6,7,8,9 (9digits)
2nd digit - since we have selected 9 natural digits for the digit we have 8 more such digits but we can use zero for 2 nd digit . (therefore 9 digits again)
3rd digit - we have 8 digits
4th digit - we have 7 digits
As you said if we have 0 for the 1st digit it will be less than 1000 ?
won`t it be ?