Consider various ways of ordering the letters in the word TENNESSEE. TENENESES, EESSENNET, TNNEESSEE, and so on. (a) How many distinguishable orderings are there

3780.  

Step-by-step explanation:

To solve this we will start by just considering the number of ways to arrange 9 objects. We can do this in  9!  ways.

However since we have 3 reoccurring letters in Tennessee namely n,s and e we need to remove the times these form the same arrangement. Let me give an example to show what this means. Lets say we have the arrangement:

ennetssee

Now what happens if we exchange the places of the letters n for example? Of course we get the same arrangement of letters. We don’t want to count these as 2 different arrangements since for our interests they are the same. We therefore divide  9!  by the number of times this type of double counting occurs.

Since the word has the letter n occurring twice we will start by diving by  2! .

The letter s occurs 2 times as well so we will have to divide by  2!  again.

Finally the letter e occurs 4 times and so we will have to divide by  4!  here.

Now we get the following result:

9/(2 x 2 x 4)=3780.  

So in conclusion there are 3780 different ways to arrange the letters in Tennessee.

school a:

minimum value is 2

maximum value is 22

the lower quartile is 2.5

the median is 10

the upper quartile is 15.5

school b:

minimum value is 9

maximum value is 20

the lower quartile is 12

the median is 16

the upper quartile is 18

box plot for school a isn't symmetrical. the data tails on the right

box plot for school b isn't symmetrical. the data tails on the left

hope i

-lavira: )