# Math Help - Arrangements

1. ## Arrangements

If 10 letter words can be formed by rearranging the letters of the word SIMPLIFIES, how many of these will the word MISS appear?

16 people are invited to a party. They are to sit around 2 circular tables, with 8 people at each table.
How many different ways can 2 groups of 8 be chosen?
Find the number of different seating arrangements that are possible at the party.

thankyou so much to anyone who can help me with these questions!

2. Originally Posted by flyinhigh123
If 10 letter words can be formed by rearranging the letters of the word SIMPLIFIES, how many of these will the word MISS appear?

16 people are invited to a party. They are to sit around 2 circular tables, with 8 people at each table.
How many different ways can 2 groups of 8 be chosen?
Find the number of different seating arrangements that are possible at the party.

thankyou so much to anyone who can help me with these questions!
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3. Originally Posted by flyinhigh123
16 people are invited to a party. They are to sit around 2 circular tables, with 8 people at each table.
How many different ways can 2 groups of 8 be chosen?

Find the number of different seating arrangements that are possible at the party.
There are $\frac{16!}{2(8!)^2}$ ways to choose the two groups.

There are $7!$ ways to seat each group at a circular table.

So what is the answer and why?