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.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?
This is a a permutation with reparation. Consider the word [imath]TENNESSEE[/imath]. How many distinct rearrangements are there?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...
Is it correct?This is a a permutation with reparation. Consider the word [imath]TENNESSEE[/imath]. How many distinct rearrangements are there?
Lets start slowly. The string [imath]E_1E_2E_3E_4[/imath] contains four distinct letters that can be arranged is twenty-four (4!) ways.
But without the subscripts [imath]EEEE[/imath] can be rearranged is only one way. So lets apply that to the other repeating letters.
[imath]TE_1N_1N_2E_2S_1S_2E_3E_4[/imath] is made of nine distinct letters ans can be rearranged is [imath]9!=362880[/imath] ways.
But without subscripts [imath]TENNESSEE[/imath] can be rearranged in [imath]\dfrac{9!}{(4!)(2!)(2!)}=3780[/imath] ways.
Now please post your answer.
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.)View attachment 28577 Is it correct?