haidzz wrote:
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?
A. Six
B. Eight
C. Ten
D. Fourteen
E. Sixteen
PS45461.01
Attachment:
2019-09-21_1430.png
If we define Pat's path in a block-by-block manner, we can see that any route from X to Y will consist of 3 UPS and 2 RIGHTS.
So for example, if we let U represent walking one block UP, and let R represent walking one block RIGHT, one possible path is URURU.
Another possible path is UUURR
Another possible path is UURUR
So our question becomes, "
In how many different ways can we arrange 3 U's and 2 R's?"
-----------ASIDE-----------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:
If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....] So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are
11 letters in total
There are
4 identical I's
There are
4 identical S's
There are
2 identical P's
So, the total number of possible arrangements =
11!/[(
4!)(
4!)(
2!)]
---------------------------------
Now let's apply the MISSISSIPPI rule to arranging 3 U's and 2 R's
There are
5 letters in total
There are
3 identical U's
There are
2 identical R's
So, the total number of possible arrangements =
5!/[(
3!)(
2!)] = 10
Answer: C
Cheers,
Brent
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