How many seven digit numbers can be formed with the digitis 1 2 4 7?

This answer is based on assumptions that indicate we want the size of a set S of numbers, the five smallest of which are 1,111,111

1,111,112

1,111,114

1,111,117

1,111,121

and the two largest of which are 7,777,774

7,777,777

The following two numbers would therefore not be in S: 1

777,777 The answer is: 47 = (4x4x4x4x4x4x4) = 16,384