Want to improve this question? update the inquiry so it's on-topic because that ptcouncil.netematics stack Exchange.

Closed 6 year ago.

You are watching: How many different arrangements of the letters in the word "color" are there?


Using every the letter of the word arrangement how countless different words making use of all letters at a time can be do such the both A, both E, both R both N happen together .


*

*

$\begingroup$ In basic if you have $n$ objects v $r_1$ objects of one kind, $r_2$ objects that another,...,and $r_k$ objects of the $k$th kind, they have the right to be i ordered it in $$\fracn!(r_1!)(r_2!)\dots(r_k!)$$ ways. $\endgroup$
"ARRANGEMENT" is one eleven-letter word.

If there to be no repeating letters, the prize would just be $11!=39916800$.

See more: How To Tame An Elephant In Mo Creatures, Mo Creatures Help Can'T Tame An Elephant

However, since there room repeating letters, we have to divide to remove the duplicates accordingly.There are 2 As, 2 Rs, 2 Ns, 2 Es

Therefore, there are $\frac11!2!\cdot2!\cdot2!\cdot2!=2494800$ ways of arranging it.


*

The word plan has $11$ letters, not every one of them distinct. Imagine the they are written on little Scrabble squares. And also suppose we have actually $11$ continuous slots into which to put these squares.

There space $\dbinom112$ ways to choose the slots wherein the 2 A"s will go. Because that each of this ways, there room $\dbinom92$ means to decide where the two R"s will go. For every decision around the A"s and also R"s, there room $\dbinom72$ means to decide whereby the N"s will go. Similarly, over there are currently $\dbinom52$ ways to decide whereby the E"s will go. That pipeline $3$ gaps, and $3$ singleton letters, which have the right to be arranged in $3!$ ways, for a complete of $$\binom112\binom92\binom72\binom523!.$$


*

Highly energetic question. Knife 10 reputation (not counting the association bonus) in order to answer this question. The reputation requirement helps defend this concern from spam and also non-answer activity.

Not the answer you're spring for? Browse various other questions tagged permutations or ask your very own question.


In how many ways can the letter of the word 'arrange' be i ordered it if the two r's and also the two a's perform not happen together?
In how many ways can the letters of native $PERMUTATIONS$ be i ordered it if over there are always 4 letters between P and also S?
*

site architecture / logo design © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.9.24.40305


your privacy

By click “Accept all cookies”, friend agree ridge Exchange deserve to store cookie on your maker and disclose details in accordance v our Cookie Policy.