# Start of script ----

# permutations and combinations

n <- 10
k <- 3

choose(10,3)

library(gtools) # R package with functions for permutations and combinations

n <- 10
k <- 3

perm01 <- permutations(n, k)
head(perm01)
dim(perm01)

combin01 <- combinations(n, k)
head(combin01)
dim(combin01)

# All CA licence plates

dim(permutations(26, 3, repeats.allowed = TRUE))[1]*dim(permutations(10, 3, repeats.allowed = TRUE))[1]

10*dim(permutations(26, 3, repeats.allowed = TRUE))[1]*dim(permutations(10, 3, repeats.allowed = TRUE))[1]

# All CA licence plates using the Tidyverse in R

library(tidyverse)

letters

numbers <- 0:9
numbers

# Old plates LLLNNN

CA_plates <- crossing(letters, letters, letters, numbers, numbers, numbers) %>% 
  unite("letters...1", "letters...2", "letters...3", "numbers...4", "numbers...5", "numbers...6", col = plate, sep = "") 
dim(CA_plates)
26^3*10^3

# New plates NLLLNNN

# Most likely will be too big for your available RAM

CA_plates <- crossing(numbers, letters, letters, letters, numbers, numbers, numbers) %>% 
  unite("numbers...1", "letters...2", "letters...3", "letters...4", "numbers...5", "numbers...6", "numbers...7", col = plate, sep = "") 
dim(CA_plates)
10*26^3*10^3

# End of script ----