Of the N^3 ordered triples, 3N^2 - 2N have a repeated entry, so the
repeat-free count is N^3 - (3N^2 - 2N), which eq (1.30) asserts
equals the falling product N(N-1)(N-2) of eq (1.6).
Arguments
- N
number of distinct objects, N >= 0.
Value
list(n_objects, total, with_repeat, no_repeat, falling_product,
forms_agree).
References
Morin, D. J. (2016). Probability: For the Enthusiastic
Beginner. Createspace. Eq. (1.30).
Examples
TripNoRep(6)$no_repeat
#> [1] 120
