How many strings of three decimal digits (0, 1, 2, …, 9)
a) do not contain the same digit three times?
b) begin with an odd digit?

Question

How many strings of three decimal digits (0, 1, 2, …, 9)
   a) do not contain the same digit three times?
   b) begin with an odd digit?

abb0t · Answer

There are $10^3$ decimal strings with 3 digits, and there are 10 of them containing three equal digits: 000, 111, 222. . .  999. Therefore, there are 1000 − 10 = 99

There are 5 odd digits, therefore u have $5 \times 10 \times 10 = 500$ strings
beginning with an odd digit.