A tricky one . . . It took a bit of Thinking.
Given the word CATERING, how many 5-letter words can be made
using at least one vowel and one consonant with repetition?
With no restrictions, there are: .8^5 possible five-letter words.
The only time we don't have at least one and one consonant
. . is when we happen to pick five consonants.
This can happen in: .5^5 ways.
Therefore, the answer is: .8^5 - 5^5 .= .32,768 - 3,125 .= .29,643