The Question Writing Commitee consists of seven volunteers from around the country who are amazingly dedicated to the Mathcounts program. This past weekend, was the last meeting for this particular group of question writers. Before the meeting, they are put into pairs, eith the seventh member pairing up with a Mathcounts staff person to make a total of four pairs. When we entered the workroom, there were four pairs of chairs around a large table. (There were two chairs together, and then a lot of space and then two chairs together and then a lot of space, and so on.) Though we could sit anywhere, we obviously had to sit with the person who was our pre-assigned partner. In how many ways could the eight people have sat around the table ensuring that each pre-assigned pair was sitting at a pre-assigned set pair of the chairs.?

Question

The Question Writing Commitee consists of seven volunteers from around the country who are amazingly dedicated to the Mathcounts program. This past weekend, was the last meeting for this particular group of question writers. Before the meeting, they are put into pairs, eith the seventh member pairing up with a Mathcounts staff person to make a total of four pairs. When we entered the workroom, there were four pairs of chairs around a large table. (There were two chairs together, and then a lot of space and then two chairs together and then a lot of space, and so on.) Though we could sit anywhere, we obviously had to sit with the person who was our pre-assigned partner. In how many ways could the eight people have sat around the table ensuring that each pre-assigned pair was sitting at a pre-assigned set pair of the chairs.?

I REALLY don't get this at all. PLEASE help.
Thanks, I appriciate it.

Answer 1

I answered basically the same question (without all the unecessary words) yesterday. Did you ask it?

Answer 2

See this previous answer of mine:

http://www.jiskha.com/display.cgi?id=1201789166

Answer 3

To solve this problem, we need to consider the different arrangements of the four pairs around the table. Let's break it down step by step:

1. Choose a pair that will sit together: Since there are four pairs, there are four options for the first pair.

2. Arrange the remaining three pairs: After the first pair is seated, there are three pairs remaining. This means there are three options for the second pair, two options for the third pair, and one option for the last pair.

3. Arrange the pairs around the table: Now that we have determined the pairs and their order, we need to arrange them around the table. However, since the chairs are set in pairs, we only need to consider the relative arrangement of the pairs, not the individuals within each pair.

To calculate the total number of arrangements, we multiply the number of options for each step together.

Number of arrangements = (Number of options for choosing the first pair) * (Number of options for arranging the remaining pairs)

Number of arrangements = 4 * 3 * 2 * 1

Number of arrangements = 24

Therefore, there are 24 different ways the eight people can sit around the table while ensuring each pre-assigned pair sits at a pre-assigned set of chairs.