# Arrangements

• Sep 6th 2009, 04:55 AM
flyinhigh123
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!
• Sep 6th 2009, 05:29 AM
garymarkhov
Quote:

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!

Read Easy Permutations and Combinations | BetterExplained and you'll never have to ask for help with combinations and permutations again (Nod)
• Sep 6th 2009, 06:04 AM
Plato
Quote:

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 $\displaystyle \frac{16!}{2(8!)^2}$ ways to choose the two groups.

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

So what is the answer and why?