Find the # of 4-letter words that can be formed from the letters in the word QUESTION under each condition:?

Question

Find the # of 4-letter words that can be formed from the letters in the word QUESTION under each condition:
a)At least 1 consonant must be used.
b)At least 1 consonant and 1 vowel must be used.
c)No two vowels can be together.

Answer 1

7

Answer 2

With no constraints, 8P4 = 1680

There are an equal number of vowels and consonants in the word QUESTION, so there is only one possibility of creating a word without at least one consonant, so under condition #1 the answer is 1679.

under condition #2, there is again one less possibility, so 1678 is the answer.