+51 Find the number of ways of choosing three people in a circular table with 12 people, so that no two people are next to each other. Use this image:
+128485 Not great at "counting" probs....here's my best attempt....corrections welcome !!!
1 3 5 6 7 8 9 10 11 7
2 4 6 7 8 9 10 11 12 7
3 5 7 8 9 10 11 12 6
4 6 8 9 10 11 12 1 6
5 7 9 10 11 12 1 2 6
6 8 10 11 12 1 2 3 6
7 9 11 12 1 2 3 4 6
8 10 12 1 2 3 4 5 6
9 11 1 2 3 4 5 6 6
10 12 2 3 4 5 6 7 6
11 1 4 5 6 7 8 5
12 2 5 6 7 8 9 5
2(5) + 8(6) + 2(7) = 72 ways
+2440 Tthe number of ways of choosing three people in a circular table with 12 people, so that no two people are next to each other.
Solution:
There are 12 ways to choose 3 persons who are adjacent (next to each other).
There are 12 ways to choose 2 persons who are adjacent.
There are 8 ways to choose 1 person who is not adjacent to the other two (2).
There are nCr(12,3) to choose a set of three persons from set of 12.
Subtract the persons who are adjacent from the total sets.
\(\text{So then ... } \dbinom {12}{3} - 12 - (12*8) = 112\\ \small \text{ There are 112 ways to select three persons from a set of 12 seated in a circle, such that no two persons are adjacent. }\\\)
GA
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