Stars and bars

Unordered picks of n objects from N types with repetition allowed: N_U_n = C(n + (N-1), N-1), eq (1.16). The equal form C(n+N-1, n) is computed as a cross-check. Worked cases: eq (1.17) n=10, N=4 -> 286; eq (1.48) n=2, N=6 -> 21; eq (1.49) n=2 -> N(N+1)/2; eq (1.50) N=2 -> n+1; eq (1.53) N=3 -> (n+1)(n+2)/2.

Usage

StarBars(n, N)

Arguments

n

number of picks.

N

number of distinct types, N >= 1.

Value

list(n_picks, n_types, count, count_alt, forms_agree).

References

Morin, D. J. (2016). Probability: For the Enthusiastic Beginner. Createspace. Eqs. (1.16)-(1.17), (1.48)-(1.50), (1.53).

Examples

StarBars(10, 4)$count
#> [1] 286