diff --git a/pkgs/racket-doc/scribblings/reference/numbers.scrbl b/pkgs/racket-doc/scribblings/reference/numbers.scrbl
index 28e2c7121c..664c1c3fdd 100644
--- a/pkgs/racket-doc/scribblings/reference/numbers.scrbl
+++ b/pkgs/racket-doc/scribblings/reference/numbers.scrbl
@@ -966,8 +966,7 @@ the @tt{RtlGenRand} system function.
          any/c]{
 
 Returns a random element of the sequence. Like @racket[sequence-length], does
-not terminate on infinite sequences, and extracts elements up to the returned
-element.
+not terminate on infinite sequences, and evaluates the entire sequence.
 
 @history[#:added "6.4"]}
 
@@ -978,12 +977,13 @@ element.
                         [#:replacement? replacement? any/c #t])
          (listof any/c)]{
 
-Returns a list of @racket[n] elements of @racket[seq], picked at random.
+Returns a list of @racket[n] elements of @racket[seq], picked at random, listed
+in any order.
 If @racket[replacement?] is non-false, elements are drawn with replacement,
 which allows for duplicates.
 
 Like @racket[sequence-length], does not terminate on infinite sequences, and
-extracts elements up to the returned element.
+evaluates the entire sequence.
 
 @history[#:added "6.4"]}
 
diff --git a/racket/collects/racket/random.rkt b/racket/collects/racket/random.rkt
index 9dcf77c2c5..5d1c431e1f 100644
--- a/racket/collects/racket/random.rkt
+++ b/racket/collects/racket/random.rkt
@@ -25,8 +25,9 @@
 (define (random-sample seq n [prng (current-pseudo-random-generator)]
                        #:replacement? [replacement? #t])
   ;; doing reservoir sampling, to do a single pass over the sequence
-  ;; (some sequences may not like multiple passes)
+  ;; (some sequences may not like multiple passes, e.g., ports)
   (cond
+   [(zero? n) '()]
    [(not replacement?)
     ;; Based on: http://rosettacode.org/wiki/Knuth's_algorithm_S#Racket
     (define not-there (gensym))
@@ -41,7 +42,7 @@
     (unless (for/and ([s (in-vector samples)])
               (not (eq? s not-there)))
       (raise-argument-error 'random-sample
-                            "integer less than sequence length"
+                            "integer less than or equal to sequence length"
                             n))
     (vector->list samples)]
    [else
@@ -57,6 +58,6 @@
                  (vector-set! samples j elt)))]))
     (unless samples
       (raise-argument-error 'random-sample
-                            "non-empty sequence"
+                            "non-empty sequence for n>0"
                             seq))
     (vector->list samples)]))