JulianMathHelp
Junior Member
- Joined
- Mar 26, 2020
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Let's say a letter is LOLIPOP, and it asks how many times you can arrange the word. Is this a permutation problem even though it has repeated countings?
The name \(\bf MISSISSIPPI\) has eleven letters, four \(S's\), four \(I's\) & two \(P's\).Let's say a letter is LOLIPOP, and it asks how many times you can arrange the word. Is this a permutation problem even though it has repeated countings?
8!/2!2! Why are the denominators factorial instead of just (4)(2)(2)? Is this a combination problem?The name \(\bf MISSISSIPPI\) has eleven letters, four \(S's\), four \(I's\) & two \(P's\).
That word can be rearranged in \(\dfrac{11!}{(4!)(4!)(2!)}\) ways.
Now you apply that to \(\bf LOLIPOP\) and post the result.
You cannot count. WHY? LOLIPOP has seven letters not eight.8!/2!2! Why are the denominators factorial instead of just (4)(2)(2)? Is this a combination problem?
There's a fairly nice explanation here.Divide by 2!2!2!? Why though?
Let's look at the word \(LOONROOM\) it has eight letters with four repeating.Divide by 2!2!2!? Why though?
I perfectly understand instances where only one letter is repeated. I was having an issue when multipel distinct letters were being repeated. I wrote my understanding, could you check it please?Let's look at the word \(LOONROOM\) it has eight letters with four repeating.
Subscript the O's, \(LO_1O_2NRO_3O_4M\). Now we have a word with eight distinct letters.
There are \(8!=40302\) ways to rearrange that one eight letter word.
\(O_2 O_1 O_4 O_3MRLN\) is just one having all the \(0's\) at the start.
Here three more: \(O_1 O_2 O_4 O_3MRLN\) \(O_4 O_3 O_2 O_1MRLN\) & \(O_4 O_1 O_2 O_3MRLN\)
That is just four of the \(4!=24\) ways to rearrange the word \(LOONROOM\) having all subscripted \(O's\) at the beginning.
So of the \(40302\) rearrangements of \(LO_1O_2NRO_3O_4M\) by dropping the subscripts we get \(4!\) identical copies.
So divide.
The logic is exactly the same.perfectly understand instances where only one letter is repeated. I was having an issue when multipel distinct letters were being repeated. I wrote my understanding, could you check it please?
By George, I think you have it.So if I received the question: How many ways can "STARWARS" be arranged, it would be 8!/(2!2!) The first 2! is to get rid of the duplicates of "S", and the second is to get rid of the duplicates of "R"'s.
How about the duplicate "A"s?So if I received the question:
How many ways can "STARWARS" be arranged, it would be 8!/(2!2!) The first 2! is to get rid of the duplicates of "S", and the second is to get rid of the duplicates of "R"'s.
I miss that one. THANKS.How about the duplicate "A"s?