Letter Arrangements: how many six-letter words can be formed

[Clifford]

I am pretty sure I am getting the hang of these, just want somebody to check this over for me, thanks.

how many six letter word can be formed using the letters from the word "stress"
A) if s's alternate with other letters?
B) if s's are all together?
C) if they begin and end with s
D) if they begin with s but do not end in s

A) SXSXSX or XSXSXS, s's can be arranged in 3 orders, x's can be arranged in 3 orders
so 2(3!)(3!) = 72
B) treat s's as one letter,
so 4! = 24
C) if it begins with s and ends with s, take two letters of out of posible arrangments
(6-2)! = 4! = 24
D) if the word begins with s, take one letter out of the possible arrangements
(6-1)! = 5! = 120
Subtract C from D, 120 - 24 = 96

 

[pka]

Re: Letter Arrangements

Part a should be 2(3!).

 

[Clifford]

Further question on part d, if you solve 6! / 3! - 5! / 2! you get 60.

I dont understand how this is the amount of words that begins with s. I understand how they don't end in s though.

To me, it would make more sense to do, 5! / 2! words start with s, which is 60, and subtract 24 from 60 since 24 is the amount of words that begin and end with s.
60 - 24 = 36.

 

[pka]

5! / 2! words start with s, which is 60, and subtract 24 from 60 since 24 is the amount of words that begin and end with s.
60 - 24 = 36.

Yes that is correct.