Refer to the figure given below. AB, CD and EF are three parallel paths. A person starts from AB to reach EF by moving in four steps - moving from AB to O1 in step 1, from O1 to CD in step 2, from CD to O2 in step 3 and from O2 to EF in step 4. If he takes a curved path in one step, he cannot take a curved path in the next step. In how many ways the person can reach EF from AB?
Explanation:
The total number of possible ways from AB to EF = 4 × 4 × 4 × 4 = 256 If a curved path is taken in a step, then the next step cannot be a curved path. Let C denotes a curved path and S denotes a straight path. Thus, the invalid paths are as follows: CCCC, CCCS, CCSC, CSCC, SCCC, CCSS, SCCS, SSCC. Thus, a total of 8 paths. Total number of arrangements for these 8 paths = 8 × 2 × 2 × 2 × 2 = 128 Thus, the total number of valid paths = 256 - 128 = 128 Hence, the answer is option A.
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.