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Please help me on my math problem, I beg my grades depend on this.?
Cyclic permutation
Mother,father and four children stand in a circle. In how many ways can they arrange themselves if mother and father stand opposite each other?
3 Answers
- roderick_youngLv 73 years agoFavorite Answer
There is only one cyclic arrangement with M (mother) across from F (father).
Then there are two spaces to the right of the mother, and two spaces to the left of the mother, so 4 spaces to fill with children.
M
C1 C2
C3 C4
F
The number of ways 4 children can be arranged in 4 spaces is 4!, that is, 4 * 3 * 2 * 1 = 24.
So 1 way (the mother and father) * 24 ways (the children) = 24
- Anonymous3 years ago
2 i think
- Steve ALv 73 years ago
There are four unknown spaces, so 4!
If clockwise and counterclockwise are not counted as different, 4!/2 = 12
