Question

From the word COMBINE, how many different 7 letter words are possible :
- with I adjacent to N?
- with alternating vowels and consonants?
-if a 5 letter word instead of 7 letter word is made from COMBINE, how many probability are that has exactly 3 consonants?

Answer 1

-with I adjacent to N
treat "IN" as a single element, so you now have to arrange 6 different elements, which is 6!
but it could be IN or NI,
so the number of arrangements is 2(6!) = 1440

- alternating vowels and consonants

Since you have 3 vowels and 4 consonants, you must start and end with a consonant to look like this
CVCVCVC
number of ways
= 4x<b>3</b>x3x<b>2</b>x2x<b>1</b>x1 , the bold represents the vowels
= 144

Give the last one a try. Let me know what you got with your reasoning.