In an 82-game NHL season, how many different final records are possible:
- If a team can either win, lose, or overtime lose each game?
This is a case of 82-combinations of a 3-set with replacement. The total number of records is:
\[C^{R}(3, 82) = C(84, 82) = C(84,2) = \binom{84}{2} = 3486\]
- If overtime losses are not possible?
Calculation is similar to the one above but from only a 2-set:
\[C^{R}(2, 82) = C(83, 82) = C(83,1) = \binom{83}{1} = 83\]