Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Think about a grid with <img alt="A" src="https://entrancecorner.oncodecogs.com/gif.latex?A

Think about a 10\times 11 grid with A as the starting point and B as the finishing point. Each step can either be an upward or a rightward movement. Find the total number of shortest paths that lead to endpoint B .

Option: 1

352716


Option: 2

552816


Option: 3

353715


Option: 4

362816


Answers (1)

best_answer

We must take 10 steps to the right and 11 steps up in order to go for the shortest distance to endpoint B . Let x and y each represent a step to the right and an upward step, respectively. Consequently, there are 10 x steps and 11 y steps in total.

These 10 xs and 11ys can be arranged in any way to find the shortest path. The binomial coefficient provides the number of possible arrangements for these steps:
{ }^n \mathrm{C}_r=\frac{n !}{r !(n-r) !}
where n denotes the overall number of steps, r the number of steps taken in one particular direction, in this case to the right, and \left ( n-r \right ) the number of steps taken in the opposite direction, in this case upwards.

Using this equation, we obtain:
\begin{aligned} & { }^{21} \mathrm{C}_{11}=\frac{21 !}{11 !(21-11) !} \\ = & \frac{21 !}{11 ! \times 10 !} \\ = & 352716 \end{aligned}
Total number of ways : 352716 . 

 

 

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

NTA Exam 2025 Live: UGC NET admit card out for all exams; JEE Main session 1 hall ticket soon
anam-khan

SFI protests across Tamil Nadu universities against UGC draft regulations on faculty recruitment
anam-khan

How to get top rank in JEE Main 2025? Last 10-day study plan

Latest Question