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


↑


North


ßWest

A

Solution follows here:
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)
Comment on puzzle3 can be verified for the logic:
ReplyDeleteDear Sankar
ReplyDeleteNice to see u r Blog. A Great Attempt. Hearty Congratulations All The Best
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