Question

A person has to move from A to B. He can only move upwards or towards the right. Find the probability that he passes through C?

• A. 1/2
• B. 10/21
• C. 13/24
• D. 1/3

Answer 1

The correct option is B 10/21

Option (b)

Totally there are 4 vertical distances and 5 horizontal distances VVVVHHHHH.

Number of ways in which a person can go from A to B via C= Arrangement of 9 things out of which 4 are identical and of one type and 5 are identical and of another type. = $\frac{9!}{4!\times 5!}=126$.

Number of ways of reaching C from A= HHVV= ${}^4{C}_2=6$. Number of ways of reaching B from C= HHHVV = ${}^5{C}_3=10$.
Required Probability = $\frac{(10\times 6)}{126}=\frac{10}{21}$