Question 97

With rectangular axes of coordinates, the number of paths from (1, 1) to (8, 10) via (4, 6), where each step from any point (x, y) isĀ either to (x, y+1) or to (x+1, y), is


Correct Answer: 3920

Solution

The number of paths from (1, 1) to (8, 10) via (4, 6) = The number of paths from (1,1) to (4,6) * The number of paths from (4,6) to (8,10)

To calculateĀ the number of paths from (1,1) to (4,6), 4-1 =3 steps in x-directions and 6-1=5 steps in y direction

HenceĀ the number of paths from (1,1) to (4,6) = $$^{(3+5)}C_3$$ = 56

To calculate the number of paths from (4,6) to (8,10), 8-4 =4 steps in x-directions and 10-6=4 steps in y direction

Hence the number of paths from (4,6) to (8,10) = $$^{(4+4)}C_4$$ = 70

The number of paths from (1, 1) to (8, 10) via (4, 6) = 56*70=3920

Video Solution

video

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 35+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

cracku

Boost your Prep!

Download App