How to judge whether list A contains all elements of list B

I want to determine whether a list A contains all the elements in the list B (including duplicate elements).

For example, for A = {1, 1, 1, 3, 3}; B = {1, 1, 1, 3, 3, 3} should return False.

For A = {1, 1, 1, 3, 3}; B = {1, 1, 1, 3} should return True.

For A = {3, 3, 1, 1, 1}; B = {1, 1, 1, 3} should return True.

For A = {3, 3, 1, 1, 4}; B = {1, 1, 4, 4} should return False.

What can I do to solve this problem succinctly?

SubsetQ[{3, 3, 1, 1, 4}, {1, 1, 4, 4}](*the result is True, which does not meet the requirements*)

In addition, I'd like to know what other ways to get the index of an array:

SeedRandom[1234]
RandomSample[Array[x, 10]]
% /. _[x_] :> x(*Besides this method, I would like to know as many methods as possible*)

You can use the ResourceFunction "MultisetInclusionQ":

ResourceFunction["MultisetInclusionQ"][{1,1,1,3,3},{1,1,1,3,3,3}]
ResourceFunction["MultisetInclusionQ"][{1,1,1,3,3},{1,1,1,3}]
ResourceFunction["MultisetInclusionQ"][{3,3,1,1,1},{1,1,1,3}]
ResourceFunction["MultisetInclusionQ"][{3,3,1,1,4},{1,1,4,4}]

False

True

True

False

ClearAll[f]
f = And @@ NonNegative[Subtract @@ (KeyUnion@(Counts /@ {##}) /. _Missing -> 0)] &;

Examples:

A1 = {1, 1, 1, 3, 3}; B1 = {1, 1, 1, 3, 3, 3};
A2 = {1, 1, 1, 3, 3}; B2 = {1, 1, 1, 3};
A3 = {3, 3, 1, 1, 1}; B3 = {1, 1, 1, 3};
A4 = {3, 3, 1, 1, 4}; B4 = {1, 1, 4, 4};

f @@@ {{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}}
{False, True, True, False}

You can also use Fold + DeleteCases as follows:

ClearAll[f2]
f2 = Fold[DeleteCases[#, #2, 1, 1] &, #2, #] === {} &;

f2 @@@ {{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}}
{False, True, True, False}

For the second part of the question:

SeedRandom[1234]
rs = RandomSample[Array[x, 10]]
{x[1], x[7], x[5], x[6], x[9], x[3], x[10], x[4], x[8], x[2]}
rs[[All, 1]]
{1, 7, 5, 6, 9, 3, 10, 4, 8, 2}
First /@ rs
{1, 7, 5, 6, 9, 3, 10, 4, 8, 2}