question_answer

In figure given, person can move towards right or in upward direction only how many ways are there to reach the point B from A

A)  70                         

B)  90       

C)  8                                            

D)  16

Correct Answer: A

Solution :

 We have shown two possible path in the figure. If horizontal movement is written as H and vertical movement is written as V. Then, these paths can be written as \[\text{H}\,\text{H}\,\text{H}\,\text{H}\,\text{V}\,\text{V}\,\text{V}\,\text{V}\]and\[\text{HV}\,\text{HV}\,\text{HV}\,\text{HV}\] Hence, energy path is basically arrangement of 4 'H' and 4 'V. \[\therefore \]Total number of ways \[=\frac{8!}{4!4!}\] \[=\frac{8\times 7\times 6\times 5\times 4}{4\times 3\times 2\times 1\times 4}\]\[=70\]