Exactly, although some strings may only use two of the notes for easier fingering mechanics (that's where patterns are formed). A cool trick to use when naming the notes of a formula is to number the notes as well.
I'll use the C Major as an example starting at the root note. C D E F G A B C D E F G A B C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Remember, a scale only has 7 notes. The 8th note is the same as the 1st or the root note with a higher pitch,
referred as an Octive ( = 8, an octopus has 8 legs)
This trick comes in handy for all sorts of things. Say the make up of a C major chord. The notes used to make a major chord are the 1st, 3rd and 5th notes of the major scale, so a C major chord would use C+E+G notes in it's composition. Cmaj7 is C+E+G+B. Notice the 2nd and the 9th are also the same and so on. This trick works for everything major. Use a minor formula of notes numbered to compose minors.
This also works for modes when moving the numbers up in position. So, if you start with D as 1, E-2, F-3, etc., through D-15, these are the notes for
D Dorian mode. Compare these notes to the ones used in a D Major scale. Notice the 3rd note in D Major is F# (# = Sharp) and the 3rd note in D Dorian mode is F. Moving the 3rd note of a major scale back a half step changes the formula and it becomes minor. So D Dorian mode would be minor and sound best in most cases when played over a D minor Chord. Chew on that for a while and you'll get some good ideas. Digest some simple formulas before jumping into the more complicated stuff such as augmented and diminished scales like the Locrian mode (diminished). You'll probably never use due to it's different sound.