Solving 2 Counting Problems: 9 Women, 6 Men & 25 Flags on 10 Poles

[ghostskwid]

Homework Statement

1. 9 women, 6 men are to be seated on a table with 15 seats, how many ways can you assign the seats if no two men are seated next to each other.?

2. How to place 25 unique flags on 10 numbered flagpole if order of the flags on a flagpole is relevant

Homework Equations

The Attempt at a Solution

1. So for one, I know that with 15 people you simply would do 15! then eliminate the cycling arrangements, or divide by 15 since ABCDEF is equal to FABCDE for 6 so you would divide by 6 to eliminate repeats. Not sure how to handle men sitting next to each other.

2. I'm not sure I understand this questions, it is worded verbatim as the instructor state it. If it's jut 10 flagpoles...it would just be 25! / 15! but...I think it might mean 10 flagpoles total and you can put flags on them in any order.

Thanks!

 

[tiny-tim]

hi ghostskwid!

1. 9 women, 6 men are to be seated on a table with 15 seats, how many ways can you assign the seats if no two men are seated next to each other.?

how many ways can you put 9 women into 6 spaces (with at least 1 woman in each space)?

2. How to place 25 unique flags on 10 numbered flagpole if order of the flags on a flagpole is relevant

they mean how to place 25 unique flags in 10 numbered boxes