s = []

for a in ('ТЬЮРИНГ'):

for b in ('ТЬЮРИНГ'):

for c in ('ТЬЮРИНГ'):

for d in ('ТЬЮРИНГ'):

for e in ('ТЬЮРИНГ'):

for f in ('ТЬЮРИНГ'):

w=a+b+c+d+e+f

if a != 'Ь' and w.count('ЮЬ') == 0 and w.count('ИЬ') == 0 and w.count('Т') <= 1 and w.count('Ь') <= 1 and w.count('Ю') <= 1 and w.count('Р') <= 1 and w.count('И') <= 1 and w.count('Н') <=1 and w.count('Г') <= 1:

s.append(w)

print(len(s))

Выведет:3120