The Cyrillic Alphabet has thirty three letters Ten are vowel

The Cyrillic Alphabet has thirty three letters. Ten are vowels, twenty one are consonants, and two are ‘signs’. For the following problems, do not compute the actual values.

(i). How many seven letter ‘words’ can be formed?

(ii). How many seven letter ‘words’ can be formed if no repetitions are allowed?

(iii).How many seven letter ‘words’ can be formed if the first and last letters must be vowels, and repetitions are not allowed?

(iv). How many seven letter ‘words’ can be formed if the first and last letters are to be ‘opposite’ signs, the middle letter a vowel, and repeats are not allowed?

Solution