The question is long, the first sentence reads as "Alicia lives in a town..."

I am completely confused on the explanation, especially the sencond part regarding the numerator, why the total blocks reduced to 4 instead of 5? If the total blocks reduced to 4, why the denominator is 3!1!, not 2!2!? How do you decide that the first block is taken for south (as reduced the number of south blocks to 1!), not for east? (which will reduce the number of east blocks to 2?)

Additonly, why Alicia only needs to make 6 decision? As explained in the text that there are only 6 blocks so she needs to make 6 decision. Does she need to make a decision at every corner of the block (except the coners in the last colum or row).

Sorry if my questions look extremely strange, I was just lost. Thanks

lkzhang, let me try to answer these and please write back if you need more clarification.

Why does Alicia need to make 6 decisions? Because she needs to walk 6 blocks home, with 3 east and 3 south, and for each block go either east or south. You are right that at each corner of a block she needs to make a decision as to where she is going to go; thus, she will make six decisions. 6!/3!3! will give us the total number of possible routes.

The problem asks us the probability of Alicia walking south the first two blocks. Once we assume she is going to walk south for the first two blocks, we know that her eventual route will look like this:
SS_ _ _ _.
Thus, we have four blocks remaining, but I know that of her six total blocks she had to walk three east and three south. We have already removed two of the south blocks (they are in places 1 and 2), so we have three east and one south block remaining.

Thus, her remaining number of combinations is:
4! (number of blocks remaining to be walked)
3! (# of east blocks remaing) 1! (# of south blocks remaining)

I hope this helps!

Thank you,

_________________
Jamie Nelson
ManhattanGMAT Instructor

A little confused!

The question asks about the probability for the first two south blocks. Why are we calculating for the remaining 3?

Because there are multiple ways in which she can walk all 6 blocks *after* walking south for the first 2 blocks. Probability is a measure of the desired outcomes / all possible outcomes, so we have to calculate all of the desired outcomes and all of the possible outcomes in order to solve.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT