Best way to make a list of a specified length of binaries with a specified number of True members

Question

I want to make a list of x zeroes and y ones in random locations. It feels like this should be doable in Mathematica in a very few characters, but my solution (which works perfectly) is relatively verbose.

I'm here using 0 and 1 rather than False and True.

exactlyNOnes[n_Integer, outOf_Integer] := Module[{list, rands},
   list = Table[0, outOf];
   While[Total[list] < n, 
    list = ReplacePart[list, RandomInteger[outOf - 1] + 1 -> 1]];
   list
   ];

I'm curious to know how wiser people would solve this.

Answer 1

Here is a (comparison of two) solutions for relatively small x+y, that I can think of.

x = 7; (* seven ones *)
y = 2; (* two zeros *)

Generate an exhaustive list and Select (36 cases):

alist = IntegerDigits[#, 2, x + y] &@Range[0, 2^(x + y) - 1];
res1 = Select[Count[#, 1] == x && Count[#, 0] == y &][alist]

{{0, 0, 1, 1, 1, 1, 1, 1, 1}, {0, 1, 0, 1, 1, 1, 1, 1, 1}, {0, 1, 1,
0, 1, 1, 1, 1, 1}, {0, 1, 1, 1, 0, 1, 1, 1, 1}, {0, 1, 1, 1, 1, 0,
1, 1, 1}, {0, 1, 1, 1, 1, 1, 0, 1, 1}, {0, 1, 1, 1, 1, 1, 1, 0, 1}, {0, 1, 1, 1, 1, 1, 1, 1, 0}, {1, 0, 0, 1, 1, 1, 1, 1, 1}, {1, 0, 1, 0, 1, 1, 1, 1, 1}, {1, 0, 1, 1, 0, 1, 1, 1, 1}, {1, 0, 1, 1, 1, 0, 1, 1, 1}, {1, 0, 1, 1, 1, 1, 0, 1, 1}, {1, 0, 1, 1, 1, 1, 1, 0, 1}, {1, 0, 1, 1, 1, 1, 1, 1, 0}, {1, 1, 0, 0, 1, 1, 1, 1, 1}, {1, 1, 0, 1, 0, 1, 1, 1, 1}, {1, 1, 0, 1, 1, 0, 1, 1, 1}, {1, 1, 0, 1, 1, 1, 0, 1, 1}, {1, 1, 0, 1, 1, 1, 1, 0, 1}, {1, 1, 0, 1, 1, 1, 1, 1, 0}, {1, 1, 1, 0, 0, 1, 1, 1, 1}, {1, 1, 1, 0, 1, 0, 1, 1, 1}, {1, 1, 1, 0, 1, 1, 0, 1, 1}, {1, 1, 1, 0, 1, 1, 1, 0, 1}, {1, 1, 1, 0, 1, 1, 1, 1, 0}, {1, 1, 1, 1, 0, 0, 1, 1, 1}, {1, 1, 1, 1, 0, 1, 0, 1, 1}, {1, 1, 1, 1, 0, 1, 1, 0, 1}, {1, 1, 1, 1, 0, 1, 1, 1, 0}, {1, 1, 1, 1, 1, 0, 0, 1, 1}, {1, 1, 1, 1, 1, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 0, 1, 1, 0}, {1, 1, 1, 1, 1, 1, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 0, 1, 0}, {1, 1, 1, 1, 1, 1, 1, 0, 0}}

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The other solution is based on Subsets and using ReplacePart for direct replacements:

replacements = Thread[# -> 0] & /@ Subsets[Range[x + y], {y}]

res2 = ReplacePart[ConstantArray[1, x + y], #] & /@ replacements // 
  Sort

res1 == res2

True