What is the number of possible words that can be made using the word “QUIZ” such that the vowels never come together?

Sure, here is the step by step solution:

Step 1: Count the number of letters in the word "QUIZ". There are 4 letters.

Step 2: Count the number of vowels in the word "QUIZ". There are 2 vowels (U, I).

Step 3: Count the number of consonants in the word "QUIZ". There are 2 consonants (Q, Z).

Step 4: Consider the vowels as a single letter. So, we have 3 letters now (Q, Z, UI).

Step 5: The number of arrangements of these 3 letters is 3! = 321 = 6.

Step 6: But the vowels (U, I) can be arranged among themselves in 2! = 2*1 = 2 ways.

Step 7: So, the total number of arrangements when vowels are together is 6*2 = 12.

Step 8: The total number of arrangements of all letters is 4! = 432*1 = 24.

Step 9: The number of arrangements where vowels never come together is the total arrangements minus the arrangements where vowels are together. So, it's 24 - 12 = 12.

So, there are 12 possible words that can be made using the word “QUIZ” such that the vowels never come together.