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Permutations and combinations [Solved!]

My question

How many words we can get from the word " gammon " .. please I want to know the style of solution>>> thanks

Relevant page

3. Permutations

What I've done so far

5×4×3×2+4×3×2

X

How many words we can get from the word " gammon " .. please I want to know the style of solution>>> thanks
Relevant page

<a href="/counting-probability/3-permutations.php">3. Permutations</a>

What I've done so far

5×4×3×2+4×3×2

Re: Permutations and combinations

Hello Karam

Firstly, it depends what we mean by "word". These are real words:

no
on
am

While these are combinations of letters, but not real words:

mma
omm
namg

Do your "words" need to be real words?

X

Hello Karam

Firstly, it depends what we mean by "word". These are real words:

no
on
am

While these are combinations of letters, but not real words:

mma
omm
namg

Do your "words" need to be real words?

Re: Permutations and combinations

at first thanks , i need the number of all Different arrangements of the letters from " gammon" .. does not require real meaning >> like from the word " sad" we can get 3×2×1 = 6 words(It is not required to have meaning) ... ....thank you again

X

at  first  thanks , i need the number of all  Different arrangements of the letters from "  gammon"  .. does not require real meaning &gt;&gt; like from the  word " sad"  we can  get 3×2×1 = 6 words(It is not required to have meaning) ... ....thank you again

Re: Permutations and combinations

Using such a definition for "word" means we would actually have 15 "words":

s
a
d
sa
as
sd
ds
ad
da
sad
sda
asd
ads
das
dsa

But actually your more precise request, "the number of all different arrangements of the letters" does imply all letters need to be present in the final arrangement.

Have you looked at Theorem 3 and Example 5 on the "Relevant page" above?

X

Using such a definition for "word" means we would actually have 15 "words":

s
a
d
sa
as
sd
ds
ad
da
sad
sda
asd
ads
das
dsa

But actually your more precise request, "the number of all different arrangements of the letters" does imply all letters need to be present in the final arrangement.

Have you looked at Theorem 3 and Example 5 on the "Relevant page" above?

Re: Permutations and combinations

thanks , but i mean all arrangements using all letters
gammon , gaommn, gnmmoa,nogmma, ect.............. i need the number of those arrangements >>> .. thank you .. plz look to this example .. How many different formalities that we can be configured from the letters of "peac".....By using the principle of counting in the permutations we find that: the number of methods for selecting the first letter is 4, the number of the methods for selecting the second letter is three ,the number of the methods for selecting the third letter is two and the number of methods for selecting the fourth letter is 1
Therefore, the number of different formalities is
4 × 3 × 2 ×1 =24
peac , paec , pcea ,....ect>>>we don't care about the meaning ....

X

thanks , but  i  mean all arrangements using all  letters  
gammon  , gaommn, gnmmoa,nogmma, ect.............. i need  the  number of  those arrangements &gt;&gt;&gt; .. thank you .. plz  look to this example .. How many different formalities that we  can be configured from the letters of  "peac".....By using the principle of counting in the permutations we  find  that: the number of methods for selecting the first letter is 4,  the number of the  methods for selecting the second letter is  three ,the number of the methods for selecting  the third letter is two and  the number of methods for selecting the fourth letter  is  1 
Therefore, the number of different formalities  is 
4 × 3 × 2 ×1  =24 
peac , paec , pcea ,....ect&gt;&gt;&gt;we don't care about  the meaning ....

Re: Permutations and combinations

Hello Karam

1. The first part of my reply was addressing your request for "words" formed from those letters, which was your opening question.

2. The second part of my reply indicated that it's now clearer what you need - arrangements of all the letters in the word "gammon".

3. The last part of my reply asked if you have read the theorem and example (in the link provided above, "3. Permutations") that will help you find your answer.

Please read that first - it will help a lot.

X

Hello Karam

1. The first part of my reply was addressing your request for "words" formed from those letters, which was your opening question.

2. The second part of my reply indicated that it's now clearer what you need - arrangements of all the letters in the word "gammon".

3. The last part of my reply asked if you have read the theorem and example (in the link provided above, "3. Permutations") that will help you find your answer.

Please read that first - it will help a lot.

Re: Permutations and combinations

thank you ,Previously i can't get
"Theorem 3 and Example 5"
then from " gammon" we can get 6!/2! = 360 Various arrangements ...
Do you agree ?

Please accept my apologies

??
??

X

thank you ,Previously i can't get  
  "Theorem 3 and Example 5"
then  from " gammon" we can get  6!/2! =  360 Various arrangements ...
 Do you agree ?
  
Please accept my apologies

?? 
??

Re: Permutations and combinations

Yes, you are correct.

More completely, we have

one g
one a
two m's
one o
one n

So the number of ways to arrange the letters in the word "gammon" is:

`(6!)/(1!xx1!xx2!xx1!xx1!)=720/2=360`

X

Yes, you are correct. 

More completely, we have

one g
one a
two m's
one o
one n

So the number of ways to arrange the letters in the word "gammon" is:

`(6!)/(1!xx1!xx2!xx1!xx1!)=720/2=360`

Re: Permutations and combinations

Thanks ..you are the best friend

X

Thanks ..you are the best friend

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