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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 only walks south or east on her way to school,

how many possible routes can she take to school?

Sagot :

To get to the school Alicia should walk 3 times south and 3 times east: SSSEEE. Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical);

Now, we wan to count all the routs which start with {SS}. So, {SS} is fixed and then there can be any combination of the rest 4 letters SEEE. So, all possible routs which start with {SS} equal to # of permutation of SEEE, which is 4!/3!=4 (# of permutations of 4 letters out of which 3 E's).

P=4/20=1/5.

Hope this helps !
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