Question

Настя составляет 6-буквенные слова из букв Т, Ь, Ю, Р, И, Н, Г, причём мягкий знак не может стоять в начале слова и после гласной. Все буквы слова различны. Сколько таких слов может составить Настя?

Answer 1

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

Answer 2

Number of 6-Letter Words that Nastya Can Form

Nastya wants to create 6-letter words using the letters T, Ь, Ю, Р, И, and Н. However, there are certain restrictions: - The soft sign (Ь) cannot be placed at the beginning of a word. - The soft sign (Ь) cannot be placed after a vowel.

To determine the number of words Nastya can form, we need to consider the possible positions for each letter.

Let's break down the problem step by step:

1. First, let's consider the position of the soft sign (Ь): - Since the soft sign cannot be placed at the beginning of a word, it has 5 possible positions: 2nd, 3rd, 4th, 5th, or 6th.

2. Next, let's consider the position of the remaining letters (T, Ю, Р, И, and Н): - Since all the letters must be different, we have 5 options for the first position, 4 options for the second position, 3 options for the third position, 2 options for the fourth position, and 1 option for the fifth position.

3. Finally, let's consider the position of the vowels (Ю, И, and Н): - Since the soft sign cannot be placed after a vowel, we need to consider the possible positions for the vowels. - If the soft sign is in the 2nd position, there are 3 possible positions for the vowels: 3rd, 4th, or 5th. - If the soft sign is in the 3rd position, there are 2 possible positions for the vowels: 4th or 5th. - If the soft sign is in the 4th or 5th position, there is only 1 possible position for the vowel: 5th.

Now, let's calculate the number of words Nastya can form:

- If the soft sign is in the 2nd position: - Number of words = 5 (options for the first position) * 3 (options for the second position) * 4 (options for the third position) * 2 (options for the fourth position) * 1 (option for the fifth position) = 120 words.

- If the soft sign is in the 3rd position: - Number of words = 5 (options for the first position) * 4 (options for the second position) * 2 (options for the third position) * 1 (option for the fourth position) = 40 words.

- If the soft sign is in the 4th or 5th position: - Number of words = 5 (options for the first position) * 4 (options for the second position) * 3 (options for the third position) * 2 (options for the fourth position) * 1 (option for the fifth position) = 120 words.

Therefore, Nastya can form a total of 120 + 40 + 120 = 280 words.