zisis wrote:
Attachment:
picture.jpg
Josh has to run an electrical wire from point a to point b along a circuit that is restricted to the grid shown to the left. How many possible paths could Josh use that have the minimum possible length?
A. 8
B. 10
C. 12
D. 15
E. 16
This is a great candidate for applying the
Mississippi RuleThe rule is useful for arranging a group of items in which some of the items are identical.
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 ONTO THE QUESTION--------
To get from point a to point b, we must travel UP (U) two times, and travel RIGHT (R) 4 times
In other words, we want to determine the number of DIFFERENT ways to arrange 2 U's and 4 R's
let's apply the above rule.
There are
6 letters in total
There are
2 identical U's
There are
4 identical R's
Total number of possible arrangements =
6!/[(
2!)(
4!)]
= 15
Answer:
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