Question

Света составляет 5-буквенные коды из букв С, В, Е, Т, А. Буквы в коде могут повторяться, использовать все буквы не обязательно, но букву С нужноиспользовать хотя бы один раз. Сколько различных кодов может составить Света С объяснением, не 1280? ​

Answer 1

Ответ:

2101

Объяснение:

Всего из это букв можно составить 3125 слов (5⁵)

Вычитаем из них количество слов без буквы С (4⁵ = 1024)

3125-1024=2101

Answer 2

To find the number of different codes that Sveta can create, we need to consider all possible combinations of 5 letters using the letters C, В, Е, Т, and А. The requirement is that the letter C must be used at least once, and there are no restrictions on the repetition of other letters or using all five letters.

To calculate this, we can use the principle of inclusion-exclusion. First, we calculate the total number of 5-letter codes without any restrictions:

Total number of 5-letter codes = 5^5 = 3125

Next, we subtract the number of 5-letter codes in which the letter C is not used at all. In this case, we can only use the remaining four letters В, Е, Т, and А:

Number of 5-letter codes without C = 4^5 = 1024

Now, we want to exclude the cases where C is not used at all, so we subtract the number of codes without C from the total:

3125 - 1024 = 2101

However, we have subtracted once the cases where C is not used, but there is one case where none of the letters are used at all (empty code). So, we need to add this case back:

Number of codes with no letters used = 1

2101 + 1 = 2102

So, Sveta can create 2102 different 5-letter codes with the given conditions.