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?

Answer 1

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.