Find the number of ways in which…….. whenever I face such type of questions, an alarm rings in my head. I fear from such questions. But today I will be giving you a simple technique to solve one such kind of a question.
Q. The question is to find the number of ways for reaching B from A. Also you cannot move upwards or towards left.
A. Never start counting the ways even if the grid is small. When you see the figure you will notice that In Order to move from A to B you have to cross x (3 in figure. 1) horizontal steps and y (3 in figure.1) vertical steps.
LET,
Horizontal steps be marked as 1
Vertical steps be marked as 0
Therefore, you need to find different combinations of 111……(x times) 00000….. (y times) binary code. Now this problem has become of Permutation and Combination in which you have to arrange the digits of a number and tell how many numbers are possible with the digit of this number. So all those people who have basics of Permutation and Combination will be able to solve this question very easily.
Solution is = (x+y)!/(x!*y!)
= (3+3)!/(3!+3!)
= 5×4 = 20 (for figure.1)
