list manipulation - How to randomly select subsets

I have a list of around 300 elements. I want to sample subsets of length 25 such that my samples are all distinct. My first inclination was to use something like RandomSample[Subsets[list, {25}], 1000], but the problem is the number of subsets of length 25 out of a 300 element set is way to big for the computer to deal with. Anyone have a nice way to do this?

Answer

This question may be a duplicate but for the time being:

list = Range[300];

The number of subsets length 25:

n = Binomial[300, 25]

1953265141442868389822364184842211512

Five samples:

samp = RandomInteger[{1, n}, 5]

{1097179597483122074395819626389736050,
 1278400886908268917844987164926797363,
 1855898035549513136165016617586671669,
 1005956584417012779260052361741534263,
 1845054078551378518016127833496347335}

Your subsets:

 Subsets[list, {25}, {#}][[1]] & /@ samp

{{10,15,57,64,65,73,82,115,120,130,133,160,161,164,178,192,196,218,223,235,238,240,267,271,290},
{12,54,58,81,90,91,115,130,146,181,189,204,205,218,222,230,233,234,235,254,256,268,281,283,284},
{33,42,45,65,78,81,85,118,151,167,172,174,202,203,207,208,211,212,223,239,246,251,254,262,267},
{9,12,35,69,72,77,79,109,113,116,141,144,158,163,195,202,221,228,230,231,254,259,267,280,292},
{32,39,49,53,62,102,104,132,135,159,164,167,169,172,191,211,244,245,253,263,265,271,282,283,286}}

Be aware that RandomInteger could produce duplicate samples however for the example given it is extremely unlikely. You can produce more an use DeleteDuplicates and Take as needed.

I think kguler's answer is the better method, and I wish I had had the insight to realize it myself, however there is still some value in the method above. Referring to subsets by a single number can make them easier to handle.

They take less space.

Comparison (e.g. for removing duplicates) requires a single numeric comparison rather than a list comparison.

A given subset is independent of the input list; only length of input and subset matter.

One can "unrank" them at any time using the third parameter of Subsets as shown above.

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