# Math Help - Combinatorial problem

1. ## Combinatorial problem

Can anyone check if my below given questions answer is correct or not...

(a) How many different strings can be formed by rearranging all the letters of the word MISSISSAUGA? Briefly justify your answer.

my ans) 9!

(b) How many of the rearrangements in part (a) contain 4 S’s in a row? Briefly justify your answer.

my ans) Permutation(8,4)

Thanks for the help!

2. Hello, robocop_911!

(a) How many different strings can be formed by rearranging all the letters
of the word MISSISSAUGA?

There are 11 letters: . $\underbrace{A\;A}_2\;G\;\underbrace{I\;I}_2\:M\;\u nderbrace{S\;S\;S\;S}_4\;U$

There are: . $\frac{11!}{2!2!4!} \:=\:415,800$ possible strings.

(b) How many of the rearrangements in part (a) contain 4 S’s in a row?

Tape the four S's together.

Then we have 8 "letters" to arrange: . $\underbrace{A\;A}_2\;G\;\underbrace{I\;I}_2\;M\;\b oxed{SSSS}\;U$

There are: . $\frac{8!}{2!2!} \:=\:10,080$ arrangements.

3. By strings, I assume the first one asks for how many arrangements can be made from the word MISSISSAUGA?.

We have 4 S's, 2 A's, 2 A's.

$\frac{11!}{2!2!4!}=415800$

Now, for the second one:

Tie the S's together as one big letter. There is 8 places to put them and then arrange the other 7 letters in $\frac{7!}{2!2!}=1260$ ways.

$\frac{8!}{2!2!}=10080$