How Many Different Ways Can The Letters Of Be Arranged

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How Many Different Ways Can The Letters Of Be Arranged

How many words with or without meaning can be made from the letters of the word CONCENTRATIONS by taking 4$ letters at a time?

In How Many Ways Can The Letters Of The Word Bilaspur Be Arranged So That Three Vowels May Never Be Put Together?

There are only $14 letters in the word. $4$ letters can be selected with $14select 4$. $4$ letters can be arranged in $4!$ way. So the ideal answer should be $ * 4!$ . But I know this answer is wrong because some letters are repeated. So how do I solve this? I appreciate any help.

See a similar question here. You can search this website for “number of arrangements using the letters of the word” and find many similar problems.

You can also use this tool where you can enter any word and it generates such questions and solutions. Answered as 4436 given below for the word concentrations

There are 9 unique letters: C, O, N, E, T, R, A, I, S. Of these letters, N has a set of $3 (appears three times), C, T, and O have a set. $2$ and all other letters appear only once.

If The Letters Of The Bring Are Permuted In All Possible Ways And The Words Thus Formed Are Arranged As In Dictionary Order. The Find The 59^th Word

Here is a long but elementary approach. Any $4$ letter word you make here has one of the following forms:

2) A pair of identical letters and $2$ different letters (different from each other and from the pair), e.g. TOTE

Obviously, none of these types overlap, and there are no words other than these types (e.g., you don’t have $4$ multiple letters, so no one-letter words), so you need to calculate how many there are for each type. , it’s easier and then add them together. See if you can do it yourself.

EDIT: I should note that this will give you the same answer Kira said, $4436$ if that helps.

In How Many Different Ways Can The Letters Of The Word

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