local read = setmetatable({}, {__index = function(t, k) local a = {} for i=1,#k do table.insert(a, '*'..string.sub(k, i, i)) end local r = io.read local u = table.unpack or unpack return function() return r(u(a)) end end})
read.N = function(N) local t={} for i=1,N do t[i]=read.n() end return t end
string.totable = function(s) local t={} local u=string.sub for i=1,#s do t[i] = u(s, i, i) end return t end
string.split = function(s) local t={} for w in string.gmatch(s, "[^%s]+") do table.insert(t, w) end return (table.unpack or unpack)(t) end
local function array(dimensi0n, default_val) assert(type(default_val) ~= 'table') local n=dimensi0n local m={}if default_val~=nil then m[1]={__index=function()return default_val end}end for i=2,n do m[i]={__index=function(p, k)local c=setmetatable({},m[i-1])rawset(p,k,c)return c end}end return setmetatable({},m[n])end
local function tostringxx(o, depth) depth = depth or 0 if depth > 10 then return "<too deep!>" end if o == _G then return "<_G>" end local indent0 = (" "):rep((depth) * 2) local indent1 = (" "):rep((depth+1) * 2) local indent2= (" "):rep((depth+2) * 2) if type(o) == 'table' then local keys = {} local types = {} for k in pairs(o) do types[type(k)] = true table.insert(keys, k) end local types_count = 0 local lasttype for k in pairs(types) do types_count = types_count + 1 lasttype = k end if types_count == 1 and (lasttype == 'string' or lasttype == 'number') then table.sort(keys) end local inside = {} for i=1,#keys do local k = keys[i] local v = o[k] if type(k) == 'string' then k = string.format('%q', k) end table.insert(inside, indent1 .. '['..tostring(k)..'] = ' .. tostringxx(v, depth + 1)) end return '{\n' .. table.concat(inside, ',\n') .. '\n' .. indent0 .. '}' else if type(o) == 'string' then o = string.format('%q', o) end return tostring(o) end end
local function richtraceback() local x = 2 while true do local info = debug.getinfo(x) if not info then break end local fname = '<' .. info.short_src .. ":" .. info.linedefined .. ">" if info.name then fname = info.name end print(info.short_src .. ":" .. info.currentline .. ": in " .. ("%q"):format(fname)) print(" LOCALS:") local p = 1 while true do local name, val = debug.getlocal(x,p) if not name then break end print(" " .. name .. ": " .. tostringxx(val, 3)) p = p + 1 end print(" UPVALUES:") for p=1,info.nups do local name, val = debug.getupvalue(info.func,p) if not name then break end print(" " .. name .. ": " .. tostringxx(val, 3)) end x = x + 1 end end
local function myassert(b) if not b then richtraceback() error("assertion failed") end end 
--
local function clone(t)
    local c = {}
    for k,v in pairs(t) do
        c[k] = v
    end
    return c
end
--
local H, W, K = read.nnnl()
local C = {}
for i=1,H do
    C[i] = read.l():totable()
end

local function getb(mh, mw)
    local b = 0
    for h=1,H do
        if not mh[h] then
            for w=1,W do
                if not mw[w] then
                    if C[h][w] == '#' then
                        b = b + 1
                    end
                end
            end
        end
    end
    return b
end

local count = 0
local function dfs(h, w, mh, mw)
    if h < H then
        h = h + 1
        dfs(h, w, mh, mw)
        local mh1 = clone(mh)
        mh1[h] = 1
        dfs(h, w, mh1, mw)
    elseif w < W then
        w = w + 1
        dfs(h, w, mh, mw)
        local mw1 = clone(mw)
        mw1[w] = 1
        dfs(h, w, mh, mw1)
    else
        local b = getb(mh, mw)
        if b == K then
            count = count + 1
        end
    end
end

dfs(0, 0, {}, {})
print(count)

Measured memory_bytes: 2828