#HomeWork#17
#Please do not post homework
#Abrar Almahmeed, March 29


# Question 1:

RandSYT:=proc(L)
local n,k,i,S,r,row,col,L1,T,j:
if L=[] then
return table():
fi:
n:=add(L[k], k=1..nops(L)):
S:=[]:
for i from 1 to nops(L) do
if i = nops(L) or L[i] > L[i+1] then
S := [op(S), [i, L[i]]]:
fi:
od:
r := S[rand(1..nops(S))()]:
row := r[1]:
col := r[2]:
L1 := L:
L1[row] := L1[row] - 1:
if L1[row] = 0 then
L1 := [op(1..row-1, L1), op(row+1..nops(L1), L1)]:
fi:
T := RandSYT(L1):
if not type(T, table) then
T := table():
fi:
T[row, col] := n:

return T:
end:

##########################################

#Question 2:

Count := 0:
for t from 1 to 10000 do
T := RandSYT([5$5]):
if assigned(T[1,2]) and T[1,2] = 2 then
Count := Count + 1:
fi:
od:
evalf(Count / 10000);

                          0.5016000000