(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How many ways are there to rearrange the letters of the word “SUPERSTITIOUS” so that...

(a) ...each T is immediately preceded by an S?

For example, “STUERSTIPIOUS” has this property, while “SUPERSTITIOUS” does not.

(b) ...the R appears between the two Ts?

For example, “SUTERSPITIOUS” has this property, while “SUPERSTITIOUS” does not.

2. Relevant equations

I am having trouble figuring out which permutations to exclude and include, and was wondering what the rules would be on using the quotient rule to divide out unnecessary permutations.

3. The attempt at a solution

For (a) I know that there are 13! ways total with each letter being distinct. I think that I need to divide 13! by 2!2! because there's two groups where the switching of the letters doesn't matter, but I am not entirely sure. I also think that I need to divide out other non-distinct permutations, such as the identical 'i's, So my conclusion was that there will be 11!/2!2!2! ways.

For (b) I'm stuck. I know that there are 13! total ways with each letter being distinct, I know that i need to divide by each letters' mulitplicities, etc. I am very unsure about the combinations of the placements of the T's and R's though. Any ideas would be great!

Note: I don't want an answer. I kinda just want pushed in the right direction. =)

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# Homework Help: Permutations of the word SUPERSTITIOUS

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