Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Take into consideration a  grid with <img alt="A" src="https://entrancecorner.oncodecogs.com/


Take into consideration a 3\times 4 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

14


Option: 2

21


Option: 3

35


Option: 4

70


Answers (1)

best_answer

We must take 3 steps to the right and 4 steps up in order to go for the shortest distance to endpoint B . Let R and Ueach represent a step to the right and an upward step, respectively. Consequently, there are 3 R steps and 4 U steps in total.

These 3 Rs and 4 Us 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} & { }^7 \mathrm{C}_4=\frac{7 !}{4 !(7-4) !} \\ = & \frac{7 !}{4 ! \times 3 !} \\ = & 35 \end{aligned}

Total number of ways : 35

Posted by

rishi.raj

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

JEE Main 2026: Wider gap in NIT cut-offs for home and other-state quotas; outsiders need better rank
anam-khan

JEE Mains 2026: Use of calculator 'not allowed’ says NTA; cites ‘typographical error' in information bulletin
anam-khan

JEE Main 2026: NIT Warangal attracts best talent with high BTech cut-offs in top, emerging branches

Latest Question