How many different 3 digit numbers can be found using 3 of the digits 6, 7, 8, 9 only once?

Question

How many different three.digit.numbers can be found using three of the digits 6, 7, 8, 9 only once in each number?

Answer 1

Consider the string 123456789  . Observe that each of the 9  digits in the string can safely be either included or not included, since failing to include a digit will not violate the increasing order of the digits. Hence, there are 2 9   possible strings that contain (0  or 1  or 2  or ... or 9  ) digits. However, we likely want to omit the case where there are 0  digits, which leaves us with a final answer of:

2 9 −1=511