A probability problem by Digi Verse
Probability
Level
3
3 teachers, 3 girls, and 3 boys are all to be seated at a round table in alternating order (so a girl, then a teacher, then a boy, then repeat, or any such repeating patterns). How many ways are there to do so? Assume that two combinations are the same if one can be rotated to the other.
The answer is 144.
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1 solution
So, first, think only of the teachers. There are three teachers, and if you lock one teacher to prevent rotation, you get 2! ways to arrange them. Now, since you have the teachers down, rotation is not possible relative to the teacher, so you have 3! ways to arrange the boys, and 3! ways to arrange the girls. However, the you must also consider that the boy may be to the right or to the left of the teacher. Therefore, you must multiply two. Then, you would get 2! 3! 3! 2, which should equal 144.