checking if two sets are equal where order doesn't matter in R?

Question

so I am trying to write a simulation to test the probability of a certain topping selection coming up when picking 4 toppings on a pizza. (total topping selection = 7)

toppings = sample(c(1,2,3,4,5,6,7),4,replace = FALSE)
certainSelection = c(1,2,3,4)

toppingsSorted = sort(toppings)

certainSelectionCounter = ifelse(certainSelection == toppingsSorted, certainSelectionCounter + 1, certainSelectionCounter)

I have the exact probability done on paper, and the above attempt is the closest i can get to it, without the sorting its worse, which tells me that this is making order matter. is there any built in functions in R that will check if 2 sets are equal where order doesn't matter?

Answer 1

Use replicate to run the simulations. From the documentation of ?replicate, my emphasis:

replicate is a wrapper for the common use of sapply for repeated evaluation of an expression (which will usually involve random number generation).

In the code below I set the pseudo-RNG seed in order to make the results reproducible.

# compare the draws with this vector
certainSelection <- c(1,2,3,4)

# number of simulations, 10K
R <- 1e5

set.seed(2022)
res <- replicate(R, {
  toppings <- sample(c(1,2,3,4,5,6,7),4,replace = FALSE)
  setequal(certainSelection, toppings)
})
mean(res)
#> [1] 0.0286

1/choose(7, 4)
#> [1] 0.02857143

^{Created on 2022-03-08 by the reprex package (v2.0.1)}