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Let C1 ,C2,........ C​​​​​​n ... Be a sequence of concentric circles . The nth circle has the radius n and it has n openings. A point P starts traveling on the smallest circle C1, and it leaves it at an opening along the normal at the point of opening to reach the next circle C2.Then it moves on the second circle C2, and leaves it likewise to reach the third circle C3 and so on . Find the total number of different paths in which the point can come out of the nth circle.

Let C1 ,C2,........ C​​​​​​n ... Be a sequence of concentric circles . The nth circle has the radius n and it has n openings. A point P starts traveling on the smallest circle C1, and it leaves it at an opening along the normal at the point of opening to reach the next circle C2.Then it moves on the second circle C2, and leaves it likewise to reach the third circle C3 and so on . Find the total number of different paths in which the point can come out of the nth circle.

Grade:12th pass

2 Answers

Falafel
11 Points
6 years ago
Ways to come out of c1 = 1Ways to come out of c1 = 2..Ways to come out of c1 = nBy permutations Total no of ways = 1.2.3...n
kapil kumar
9 Points
4 years ago
There are r openings to come out of the rth circle and after that it can travel clockwise or anticlock wire to enter the (r+1)th circle
This, the number of paths 
     =(1.2)×(2.2)×(3.2)×...×{(n-1)}.2}× {n.2}
     =n!. 2n

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