SOLUTION: How do you do questions involving permuations where two things are arranged in alternative positions. e.g.) How many ways can you arrange the letters in the word TRADE if the vowe

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Question 1112310: How do you do questions involving permuations where two things are arranged in alternative positions.
e.g.) How many ways can you arrange the letters in the word TRADE if the vowels and consonants have to be in alternative positions?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The number of items in the two categories of items to be alternated
have to be the same of differ by 1.
As TRADE has 2 vowels, 3 consonants,, the arrangements would have to start and end with a consonant.
You have 3 consonants to arrange and 3%21=3%2A2=6 ways to arrange them.
You have choices for the order of the vowels.
You can make 6%2A2=12 arrangements where you use all 5 letters in TRADE,
while alternating vowels and consonants.
If you try to do the same with the word TIRADE, you would have
6 choices for thew order of the vowels,
6 choices for thew order of the vowels,
and 2 choices for what kind of letter to start with,
for 2%2A6%2A6=72 arrangements made with all the letters in TIRADE,
alternating vowels and consonants.