Pwayjoker27 Posts: 3, Reputation: 1 New Member #1 Aug 9, 2010, 11:11 AM
Difficult Distinguishable Permutation Problem
Consider three-letter "words" to be formed by using the vowels a, e, I, o, and u. How many different words without repetitions can be formed whose letters at the ends are you and I? I need a detailed explanation as well. Thanks!
 ebaines Posts: 12,131, Reputation: 1307 Expert #2 Aug 9, 2010, 11:42 AM

Consider first the case of the letter u being last. That means that the letters a, e, I, and o can be used in any order for the first four letter positoins. For the first position you can put any one of these 4 lettrers. After picking one for the first position, for the second position you have three remainingg letters from which to choose. Then for the third position there are two letters left, and for the fourth position you have just one choice left. So the number of ways you can select 4 letters without repeats is 4 x 3 x 2 x 1 = 24. That's how many ways you can arrange a, e, I, and o as the first four letters and have u at the end.

Now go through the same process to determine how many words you can make that have the letter I at the end. What do you get? Now add together the two answers, to get the total number of words that can have either I or u at the end.

Post back with what you get as a final answer.

**EDIT ** I may have misinterpreted the problem - see my next post.
 ebaines Posts: 12,131, Reputation: 1307 Expert #3 Aug 9, 2010, 11:50 AM

It may be that I miisunderstood the problem - rather than meaning the last letter can be either I or u, it may be that the problem asks how many 5-letter words can you make up whose fourth and fifth letters are I and u. That's different than what I wrote in my previous post. Given that the letter a, e, and o must be used in the first three positions, that gives you 3 x 2 x 1 =6 combinations for the first three positions. The last two letters can be arranged either as iu or as ui. That's 2 ways to arrange the last two letters. So the total numer of ways that the two sets of letters can be arranged is... what? Can you finish it from here? It would be a good idea to write out all possible combinations, to make sure you get it correct.
 galactus Posts: 2,271, Reputation: 282 Ultra Member #4 Aug 9, 2010, 11:52 AM

I believe it means placing a u and I on each end.

Like so,

u*i

Or

I*u
 Pwayjoker27 Posts: 3, Reputation: 1 New Member #5 Aug 9, 2010, 12:21 PM

The answer is 6---I checked, but I still don't understand how to get that answer.
 ebaines Posts: 12,131, Reputation: 1307 Expert #6 Aug 9, 2010, 12:32 PM

It would really help if you would copy the problem wording exactly as it was given to you to help clear up some of the confusion.

The only way the answer can be 6 is if it's required that the first letter be u and the last letter be I (or maybe it's the other way around). The middle three letters are then a,e, and o, which as shown previously can be arranged in 6 different ways. You can easily write out all possible combinations.
 Pwayjoker27 Posts: 3, Reputation: 1 New Member #7 Aug 9, 2010, 01:24 PM

The original way I copied it is exactly how it was given. It is very vague.

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