Answer
a) 5040
b) 5000
c) 36
Work Step by Step
a) do not contain the same digit twice?
The first digit has ten possibilities, and then the second digit has nine possibilities, as there is no repetition. The third digit has eight possibilities, and the fourth digit seven possibilities. So we have to multiply 10 x 9 x 8 x 7, which gives us 5040.
b) end with an even digit?
The first 3 digits all have ten possibilities to be any number, and the last digit only has five possibilites, this is due to the fact that it has to be an even digit. Therefore, we have to multiply 10 x 10 x 10 x 5, which gives us 5000.
c) have exactly three digits that are 9s?
There's nine possibilities for a non nine digit. So the told number of strings of digits here is 9 x 4, which gives us 36.
