SOLUTION: in how many ways can the letter of the word "HELL" be permuted, if the two 2LLs must always be apart.

Question 1165255: in how many ways can the letter of the word "HELL" be permuted, if the two 2LLs must always be apart.
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

There are 4! = 4*3*2*1 = 24 permutations of 4 letters, in all. From this amount, subtract those permutations, where two letters "L" go together. The number of such permutations is 2*3! = 2*6 = 12. The difference 24 - 12 = 12 is the number of wanted permutations in your problem. ANSWER

Solved.

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On Permutations, see introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems
    - Problems on Permutations with restrictions

    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
There are 4!/2 = 12 unique arrangements of the letters "HELL" (because the L's are indistinguishable).

From this, we must subtract 3! = 6 cases where the L's are together. Thus there are 12-6 = arrangements meeting the requirement.
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