25 of King Arthur's Knights are seated at their customary round table. Three of them are chosen at random and are sent off to slay a dragon. What is the probability that at least 2 of the 3 had been sitting next to each other?
2006-11-28 15:51:38 · 1 answers · asked by juanes34 2 in Science & Mathematics ➔ Mathematics
Pick one knight anywhere.
If you pick either of the knights directly adjacent to him, you are done. This happens 2/24 of the time.
....OOXXOO...
If you pick a knight that is separated by exactly one seat (2/24 of the time), then there are 3 out of 23 seats that are adjacent.
...OXOXO....
If you pick a knight that is more than one seat away (20/24), then there are 4 out of 23 seats that are adjacent.
...OXO...OXO...
So the probability is:
1/12 + 1/12 * 3/23 + 10/12 * 4/23
Adding it up:
23/276 + 3/276 + 40/276, or 66/276 = 33/138
This is approximately 23.91%
2006-11-28 15:56:15 · answer #1 · answered by Puzzling 7 · 1⤊ 1⤋