Question

How many three-letter arrangements can be made from the word VERTICAL if no letter can be used more than once and each arrangement is made up of a vowel between two consonants

Answer 1

Answer: 60 arrangements.

Step-by-step explanation: Since VERTICAL has 3 vowels and 5 consonants, and you need 1 vowel and two consonants, its (3 choose 1) and (5 choose 2), then times the arrangements of the consonants. The arrangements is times 2 because the different consonants can either be on the left or the right. For example, it can be VER or REV.

So, the answer is 3 times ((5 choose 2) times 2), which is 3(2(5!/(2! times 3!))), or 3(2(10)), or 60.