Hello, our class got a question from our teacher which has to do with probability.
"If three couples randomly sit down at a round table, what is the probability in order that nobody sits down with their partner?"
I have been trying to figure this out and I will do my best to explain how far I have come (English not first language).
I drew in paint how I am thinking;
< link to objectionable page removed >
(very bad at paint)
The round rings and letters symbolizes each person. For example person "A" cant sit next to person "a" because they are the couple. So person "a" can only sit in three places from all five. (3/5)
Person "B" has four choices because he/she can sit where he wants except for where person "A" and person "a" are sitting. (4/4)
Person "b" actually only has one choice because the other choice will make couple "Cc" sit next to each other. (1/3)
Eventually when I calculated all this I got it to 10% probability for no couple to sit with their partners. But I only tried one example, is there a better way to doing this?
Thanks in advance!
"If three couples randomly sit down at a round table, what is the probability in order that nobody sits down with their partner?"
I have been trying to figure this out and I will do my best to explain how far I have come (English not first language).
I drew in paint how I am thinking;
< link to objectionable page removed >
(very bad at paint)
The round rings and letters symbolizes each person. For example person "A" cant sit next to person "a" because they are the couple. So person "a" can only sit in three places from all five. (3/5)
Person "B" has four choices because he/she can sit where he wants except for where person "A" and person "a" are sitting. (4/4)
Person "b" actually only has one choice because the other choice will make couple "Cc" sit next to each other. (1/3)
Eventually when I calculated all this I got it to 10% probability for no couple to sit with their partners. But I only tried one example, is there a better way to doing this?
Thanks in advance!
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