documentclass[12pt]{article}
usepackage[utf8]{inputenc}
usepackage[english]{babel}
usepackage{listings}
usepackage{enumitem}

usepackage{etoolbox}
usepackage{pgfkeys}
usepackage{pgfmath}

% code for generating a random permutation
newcounter{randomListLength}%   current length of our random list
newcounter{randomListPosition}% current list index
newcounter{newRandomListElementPosition}% position to insert new element
% insert #1 into the next position of newRandomList unless the position
% index randomListPosition is equal to newRandomListElementPosition in
% which case the newRandomListElement is added first
newcommandrandomlyInsertElement[1]{%
  stepcounter{randomListPosition}%
  ifnumvalue{randomListPosition}=value{newRandomListElementPosition}%
    listxaddnewRandomList{newRandomListElement}%
  fi%
  listxaddnewRandomList{#1}%
}
% randomlyInsertInList{list name}{new list length}{new element}
newcommandrandomlyInsertInList[3]{%
  pgfmathparse{random(1,#2)}%
  setcounter{newRandomListElementPosition}{pgfmathresult}%
  ifnumvalue{newRandomListElementPosition}=#2relax%
    listcsxadd{#1}{#3}%
  else%
    defnewRandomList{}% start with an empty list
    defnewRandomListElement{#3}% and the element that we need to add
    setcounter{randomListPosition}{0}% starting from position 0
    xdefcurrentList{csuse{#1}}
    forlistlooprandomlyInsertElementcurrentList%
    csxdef{#1}{newRandomList}%
  fi%
}

% define some pgfkeys to allow key-value arguments
pgfkeys{/randomList/.is family, /randomList,
  environment/.code = {globalletcsbeginRandomListEnvironment{#1}
                       globalletcsendRandomListEnvironment{end#1}
                      },
  enumerate/.style = {environment=enumerate},
  itemize/.style = {environment=itemize},
  description/.style = {environment=description},
  seed/.code = {pgfmathsetseed{#1}}
}
pgfkeys{/randomList, enumerate}% enumerate is the default

% finally, the code to construct the randomly permuted list
makeatletter
newcounter{randomListCounter}% for constructing randomListItem@<k>'s

% useRandomItem{k} prints item number k
newcommanduseRandomItem[1]{csname randomListItem@#1endcsname}

% setRandomItem{k} saves item number k for future use
% and builds a random permutation at the same time
defsetRandomItem#1par{stepcounter{randomListCounter}%
       expandafterprotected@xdefcsname randomListItem@therandomListCounterendcsname{noexpanditem#1}%
       randomlyInsertInList{randomlyOrderedList}{therandomListCounter}{therandomListCounter}%
}%
letrealitem=item
makeatother
newenvironment{randomList}[1][]{% optional argument -> pgfkeys
  pgfkeys{/randomList, #1}% process optional arguments
  setcounter{randomListLength}{0}% initialise length of random list
  defrandomlyOrderedList{}% initialise the random list of items
  % Nthing is printed in the main environment. Instead, item is
  % used to slurp the "contents" of the item into randomListItem@<counter>
  letitemsetRandomItem%
}
{% now construct the list environment by looping over the randomly ordered list
  letitemrealitem
  setcounter{randomListCounter}{0}
  beginRandomListEnvironmentrelax
    forlistloopuseRandomItemrandomlyOrderedList
  endRandomListEnvironment
}

% test compatibility with enumitem
usepackage{enumitem}
newlist{Testlist}{enumerate}{1} %
setlist[Testlist]{label*=alph*.}
setlist{nosep}parindent=0pt% for more compact output

lstset{
basicstyle=bfseriesscriptsizett,
}

begin{document}
LARGE
begin{center}
    Do the following give categorical, discrete, or continuous responses?
end{center}
begin{randomList}
    item 1

    item 2

    item 3

    item 4

    item 5

    item 6

    item 7

    item 8

    item 9

    item 10

end{randomList}
end{document}