Puzzle-28 (CAT-2004)

In the below figure, the lines represent one way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?

B
						↑
						North
					ßWest	A

(1)15               (2)56               (3)120             (4)336
Solution follows here:

Solution:

The number of Horizontal lines required to reach B = 5

The number of Vertical lines required to reach B     = 3

H         H         H         H         H         V          V          V

Observe that whatever the path taken to reach B starting from A, the number of horizontal lines required is 5 and vertical lines required is 3. The beauty here is mathematically we need to find different combinations of these 5+3 = 8 lines

This is nothing but the number of ways of arranging (p+q) things where p things are of similar type and q things are of similar type. Formula here is (p+q)! / (p!q!)

∴Number of ways = (5+3)!/(5!3!) = 8!/(5!3!) = 8*7*6/3*2 = 56

Answer (2)