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tosscoin <- function(n) {
  df <- expand.grid(replicate(n, c("cara", "sello"), simplify = FALSE),
              KEEP.OUT.ATTRS = FALSE,
              stringsAsFactors = FALSE)
  
  names(df) <- paste0("X", seq_len(n))
  return(df)
}

tosscoin(3)

##      X1    X2    X3
## 1  cara  cara  cara
## 2 sello  cara  cara
## 3  cara sello  cara
## 4 sello sello  cara
## 5  cara  cara sello
## 6 sello  cara sello
## 7  cara sello sello
## 8 sello sello sello

urnsamples <- function(x, size, ordered = TRUE, replace = FALSE) {
  if (ordered) {
    # Producto cartesiano
    expand.grid(replicate(size, x, simplify = FALSE),
                KEEP.OUT.ATTRS = FALSE)
  } else {
    # Combinaciones sin orden
    combn(x, size, simplify = FALSE) |>
      do.call(what = rbind)
  }
}

urnsamples(1:3, size = 2, ordered = FALSE, replace = FALSE) 

##      [,1] [,2]
## [1,]    1    2
## [2,]    1    3
## [3,]    2    3

nsamp <- function(n, k, replace = FALSE, ordered = TRUE) {
  if (ordered) {
    if (replace) {
      return(n^k)  # Producto cartesiano con repetición
    } else {
      return(factorial(n) / factorial(n - k))  # Permutaciones sin repetición
    }
  } else {
    if (replace) {
      return(choose(n + k - 1, k))  # Combinaciones con repetición
    } else {
      return(choose(n, k))  # Combinaciones sin repetición
    }
  }
}

factorial(5)                   #A) Factorial

## [1] 120

nsamp(n = 5, k = 5, replace = FALSE, ordered = TRUE)

## [1] 120

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