Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?  Choose the most appropriate option
A) 1/3  B) 1/5  C) 1/6  D) 1/7  E) 2/5
Total number of ways to go home, considering that the order order matters =   Options: SSSEEE   Slots : ------   total permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2   Total ways to select "South" in the first 2 positions and anything else in the subsequent 4 positions =   Options: SS ????   Slots: -- ----   Permutations of 3 "S" in 2 slots AND Permutations of 4 Choices in 4 slots =   3P2 * 4P4 = 3! * 4! = 3*2*4*3*2   The probability is therefore:   3P2 * 4P4 = 6P6   3*2*4*3*2= 1/5   ANSWER:1/5
<result>B</result>
Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?