How many strings of five decimal digits

a. begin with an odd digit?

my answer) $\displaystyle 5.10^3 $

b. do not contain the same digit twice?

my answer) $\displaystyle 10.9.8.7.6$

c. have exactly three digits that are 9s?

my answer) $\displaystyle 90 $

that's 5.2=10 places for remaining 9 digits

and 9 choices for each place = 10x9 = 90, but,

can't it be like this....

exactly 3 same digits means $\displaystyle 9^3.10^2$?

d. contain exactly three distinct digits?

my answer) 10.9.8.7.10