ANYONE HELP ME!! TOPIC : PERMUTATION

[Matjek123]

In how many ways can the letters of the word "SATTLE " be arranged?
a)How many end with A?
b)How many do not end with A?

 

[pka]

It is the policy of this forum to help those who help themselves.
Therefore you need to post some of your work. Then we will check it.

 

[Dr.Peterson]

In how many ways can the letters of the word "SATTLE " be arranged?
a)How many end with A?
b)How many do not end with A?

Have you learned any formulas or methods for this sort of problem? Please show some sort of work so we can see where you need help, or else ask a specific question about it.

 

[R.M.]

How many choices do you have for the last letter? Once you figure that out, then ask yourself how many choices are left for the first letter? Second letter? etc...

 

[pka]

How many choices do you have for the last letter? Once you figure that out, then ask yourself how many choices are left for the first letter? Second letter? etc...

This is a a permutation with reparation. Consider the word $TENNESSEE$. How many distinct rearrangements are there?
Lets start slowly. The string $E_1E_2E_3E_4$ contains four distinct letters that can be arranged is twenty-four (4!) ways.
But without the subscripts $EEEE$ can be rearranged is only one way. So lets apply that to the other repeating letters.
$TE_1N_1N_2E_2S_1S_2E_3E_4$ is made of nine distinct letters ans can be rearranged is $9!=362880$ ways.
But without subscripts $TENNESSEE$ can be rearranged in $\dfrac{9!}{(4!)(2!)(2!)}=3780$ ways.
Now please post your answer.

 

[Matjek123]

This is a a permutation with reparation. Consider the word $TENNESSEE$. How many distinct rearrangements are there?
Lets start slowly. The string $E_1E_2E_3E_4$ contains four distinct letters that can be arranged is twenty-four (4!) ways.
But without the subscripts $EEEE$ can be rearranged is only one way. So lets apply that to the other repeating letters.
$TE_1N_1N_2E_2S_1S_2E_3E_4$ is made of nine distinct letters ans can be rearranged is $9!=362880$ ways.
But without subscripts $TENNESSEE$ can be rearranged in $\dfrac{9!}{(4!)(2!)(2!)}=3780$ ways.
Now please post your answer.

Is it correct?

 

[Dr.Peterson]

View attachment 28577 Is it correct?

For (b), what if it ends with T? Doesn't that change things? (I'm not saying your answer is wrong, but that I'm not sure of your reasoning based on what you wrote.)

Also, there are actually three questions there; even if you aren't expected to answer the first (the total number of arrangements), it could be useful as part of answering (b), or at least checking it.

 

[pka]

From your posted work it seems that you are making it too hard.
If we remove the $A$ from $SATTLE$ we have $STTLE$
left which can be arranged $\dfrac{5!}{2!}$ ways, that answers (a).

For (b) $\dfrac{6!}{2!}-\dfrac{5!}{2!}$.