SOLUTION: Question: In how many ways we can select 4letters from the letters of MISSISSIPPI?
My work so far:
Words with 4 different letters C(4,4)..................................24
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Question 1174360: Question: In how many ways we can select 4letters from the letters of MISSISSIPPI?
My work so far:
Words with 4 different letters C(4,4)..................................24
Words with all 4 same letters..........................................02
3 letters alike and 1 another letter... 2 x 3 .........................06
2 letters alike and 2 letters alike...C(3,1) X C(2,1).................06
2 letters alike and 2 letters different... C(3,1) X C(3,2)...........09
Answer: The total number of words is 47
Where am I going wrong? Everywhere I look there are as many different answers!!
Please help.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
start with 11 letters that are unique, and that would be 11!
but M is alone and there are 4 I, 4 S, and 2 P (and 1 M)
These lower the count since they are not unique
11!/4!2!4!!!
or 11!/1152=34650 ways
Answer by ikleyn(52816) (Show Source): You can put this solution on YOUR website!
.
(1) The formulation of the problem in your post is incorrect.
You will not understand the solution, until you learn how to formulate the problem correctly.
(2) For correct formulation and solution of similar (TWIN) problems see the link
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173142.html
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173142.html
(3) To learn the subject in more details, see my lesson
- Arranging elements of sets containing indistinguishable elements
in this site.
Happy learning (!)
==============
Comment from student: Question 1174360 Do you mean the question is not well formulated?
My response. Yes, exactly, the question IS NOT WELL FORMULATED.
The STANDARD formulation of this class of problems (and this concrete problem specifically) is THIS
How many DISTINGUISHABLE words can be formed using the letters of the word MISSISSIPPI ?
See and learn from the sources that I provided for you in my post above.
Thank you for asking.
It was VERY RIGHT STEP from your side to ask this question.
To understand these problems IN FULL, you need to learn two conceptions:
"distinguishable words" and "multiplicity of a letter in a word".
All explanations you will find in my sources, referred above.
/\/\/\/\/\/\/\/
As my gift to you for asking your question, consider these lessons on PERMUTATIONS
- 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
- Arranging elements of sets containing indistinguishable elements
- Persons sitting around a cicular table
- Combinatoric problems for entities other than permutations and combinations
- Fundamental counting principle problems
- Nice recreational problems on permutations
- 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.
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