A circular garden divided into 10 equal sectors needs to be planted with flower plants that yield flowers of 3 different colors, in such a way that no two adjacent sectors will have flowers of the same color. The number of ways in which this can be done is
Correct Answer: 1026
Solution
Colouring the sectors of a circle so that neighbours differ is the same as properly colouring a cycle with 10 vertices. The number of ways with $$k$$ colours is $$(k-1)^n + (-1)^n (k-1)$$. With $$n = 10$$ and $$k = 3$$ this is $$2^{10} + 2 = 1026$$.
Get AI Help
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Enter OTP
Didn't receive the OTP?
