<p>They give u a pic with a circle and put 8 chairs labeled 1-8 around the circle. Question is if two students are to sit directly opposite each other, leaving other chairs empty, how many such arrangements of the two students are possible? I got 4 answer is 8. Why does order matter?</p>
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<p>If the answer is 8, it would count all the people, not just the pairs of people. </p>
<p>Instead of thinking of it as a pair of people, think about it as person A and person B. How many different seats can person A sit in if person B is always opposite of him. </p>
<p>So there would be a guy in seat 1 and seat 5. </p>
<p>Seats 2 and 6
Seats 3 and 7
Seats 4 and 8
Seats 5 and 1
Seats 6 and 2
Seats 7 and 3
Seats 8 and 4</p>
<p>There’s 4 possible pairs of chairs, that aspect of your answer is correct. However, for each pair of chairs, there’s two configurations for the two people (guy 1-seat1, guy 2-seat2 or guy1-seat2, guy2-seat 1)</p>
<p>4 pairs * 2 configurations/pair = 8 configurations.</p>
<p>Why isnt guy 1 opp of guy 2 and guy 2 opp of guy 1 the same?</p>
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<p>Bump</p>
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<p>Let’s call the chairs A-H, and the people 1-8. </p>
<p>Say person 1 sits on chair A, and person 2 sits on chair B.
In another instance, person 1 sits on chair B, and person 2 sits on chair A. </p>
<p>These are two different possibilities, as the two people are sitting on different chairs in each instance. I hope you understand this.</p>
<p>You could also apply the counting principle, where step-by-step you ask yourself “how many choices are there, NOW?”</p>
<p>So when the two students come to the table, whoever chooses their seat first has 8 options. Then, when the next student goes to choose his seat, he has only 1 option – he has to choose the seat directly across from where the first kid sat!</p>
<p>Now that we are done making decisions, just multiply:</p>
<p>8 x 1 = 8.</p>
<p>Thanks!!!</p>
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