simple counting or fundamental counting? That my friend is my question.?

Question

how many four- digit numbers can be formed under the following conditions?

a) the leading digit cannot be zero

b) the leading digit cannot be zero and no repetion of digits is allowed

c) the leading digit cannot be zero and the number must be less than 5000

d) the leading digit cannot be zero and the number must be even

Answer 1

a) the leading digit cannot be zero
9*10^3 = 9,000

b) the leading digit cannot be zero and no repetion of digits is allowed
9*9*8*7 = 4,536

c) the leading digit cannot be zero and the number must be less than 5,000
4*10^3 = 4,000

d) the leading digit cannot be zero and the number must be even
9*4*10^2 = 3,600

Answer 2

a.) 9*10*10*10=9000
1st digit-Nine choices, 1-9
Remaining digits-Ten choices, 0-9

b.) 9*9*8*7=4536
1st digit-Nine choices, 1-9
2nd digit-Nine choices, 0-9 except the one used for 1st digit
3rd digit-Eight choices, 0-9 except two used for first two digits
4th digit-Seven choices, 0-9 becuase three numbers have already been used

c.)4*10*10*10=4000
1st digit- Four choices 1, 2 ,3 , or 4
Remaining digits- Ten choices, 0-9

d.)9*10*10*5=4500
1st digit- Nine choices, 1-9
2nd and 3rd digits- Ten choices, 0-9
4th digit- Five choices, 0, 2, 4, 6, or 8