If the first setting is 0 then second cannot be 0,1,2.

Therefore, there are 57 choices for the second setting and 60 for the third.

The same can be said if the first is 59.

If the first setting is 1 then second cannot be 0,1,2,3.

Therefore, there are 56 choices for the second setting and 60 for the third.

The same can be said if the first is 58.

For any number other than 0,1,58,59 all 56 of them, we exclude 5 possiblies of the second setting.

That means we can choose 55 values for the second and 60 for the third.

. The textbook is correct.