In city A, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take?
Is there any formula to find out directly??	Choose the correct choice from the following options.
A) 6 B) 66 C) 72 D) 126 E) 262
Center of the park is much important in this problem.   To pass through the park one must have to pass through this point and further to destination.   Ans = Total possible paths to destination(TPPD) - paths passing through the park (PPTP)   All possible paths covering min distance are permutation of pattern RRRRRUUUU R-&gt; One step right / U-&gt; One step up   Thus   TPPD = 9!/(5!x4!) = 126 (direct formula of permutation applied)   I have calculated PPTD in two steps first find all paths from origin to center of park:   1. Possible moves RRRUU total permutations 5!/(3!x2!) = 10   2. From park center to destination, in moves RRUU, total permutations as 4!/(2!x2!)=6.   Thus PPTD= 10 X 6 = 60   Ans = 126 -60= 
<gadget id="calculator">126 -60</gadget>
<output>66</output>
66   ANSWER:66
<result>B</result>
In city A, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take?
Is there any formula to find out directly??