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There are 6 roads between A and B and 4 road between B and C (a)in how many ways can one drive from Ato C and back to A, passing through B on both trips (B)In how many ways can one drive the circular Trip describe in ( a) without using the same road more than once

There are 6 roads between A and B and 4 road between B and C
(a)in how many ways can one drive from Ato C and back to A, passing through B on both trips
  (B)In how many ways can one drive the circular 
Trip describe in ( a) without using the same road more than once

Grade:12th pass

1 Answers

Arun
25757 Points
4 years ago
a) 6 * 4 = 24 different ways 
b) 24 * 24 = 576 ways 
c) 24 * (3 * 5) = 360 ways 

a) it's 6*4 because there are 6 different roads to get to B, then after getting there, can take 4 different paths. So every one road to B has 4 different possible paths. 

b) roundtrip is just the number of possible ways to get there, and then possible ways going back. 
But, you can take a different way back for each one of the 24 paths you could have taken to get to C. So it's 24 * 24. 

c) it's 24 paths the first way. Then since you can't use the same path on the way back, you take the original path out of the equation. So instead of ( 6 * 4 ), it's ( 6 - 1 ) * ( 4 - 1 ) or ( 5 * 3 ).

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