Permutations Part 2! 

 

Time to have some fun! ..do work!

My name is Aldrin and this is the second blog post of our class!  Yaaaaaaaaaaaaayyyyy!                           fun            LETS START.

This is the second part to our lesson of Permutations. If you have not already, learn the first part of Permutations from Billy Hong's last post!  http://precalculus40ssectioncwinter2015.blogspot.ca 

As we know already, Permutations is about arrangements. In order to arrange things in specific order we have an option to use either the Permutation Formula or the Dash Method. 

Permutations Formula: We can only use this formula if there are *no restrictions or repetitions* in the question.

* Assume that there are no repetitions unless stated otherwise.  

This is a secret.

Dash Method: This Method is great because it works for all situations! Just read the question carefully. ( I like this method more. )  

** With Restrictions and Repetitions we get fewer permutations**
- Restrictions are when there are specific locations to place your item. 
- Repetitions are when items are allowed to be "placed/picked/used" more than once.

Let's say there's a total of 3 apples, 2 red and 1 green. Let us find how many ways we can arrange them. Since there are 2 red apples it is considered a repetition. This means it limits us from more arrangements because two of our items are identical. 

O O O    As you can see there can only be 3 possible arrangements.  Even if you switch
O O O   the two red apples it would not add any permutations.         
O O O

**Total Arrangements * = n!/a!b!c!... **       3!/2!= 3 
n!= the overall amount of items.   
a!/b!/c!... = repeated items.  

EXAMPLES!!!!  Mr. Piatek is a great teacher.

1.) Ann wants a short playlist of songs to accompany her while studying for PreCal 40S. Her super hip phone contains 10 songs.

 i.)How many arrangements can she have using all of her songs?

ii.)With only 6 songs? 

iii.)Using only 8 songs with no repetition with the exception of her favourite song, which has to be the first and last thing she hears? 

i.) 10P10 = 10!= 3,628,800                      ii.)10P6 = 10!/10!- 6!= 10!/4!= 10x9x8x7x6x5=151,200

Dash Method:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800     10 x 9 x 8 x 7 x 6 x 5= 151,200

1s x 2s x 3s x 4s x 5s x 6s x 7s x 8s x 9s x 10s                              1s x 2s x 3s x 4s x 5s x 6s 

1s = Possible amount of songs to be placed 1st on the playlist 

2s= Possible amount of songs to be placed 2nd... 

3s= Possible amount of songs to be placed 3rd... etc. 

iii.) 1 x 9 x 8 x 7 x 6 x 5 x 4 x 1 =60,480   This question is tricky. 

           1s x 2s x 3s x 4s x 5s x 6s x 7s x 8s 

2.) In order to prevent cheating during exams, the teachers prepare a sitting plan that does not allow students who are in the same grades to sit beside each other. In one row, there were 4 grade 12 and 4 grade 11 students. how many arrangements are possible while following the sitting plan? 

4 grade12 x 4 grade11 x 3 grade12 x 3 grade 11 x 2 grade12 x 2 grade11 x 1 grade12 x 1 grade11

=576

4 grade11 x 4 grade12 x 3 grade11 x 3 grade 12 x 2 grade11 x 2 grade12 x 1 grade11 x 1 grade12

= 576

576 + 576 = 1,152

3.) How many permutations can be done using all the letters in each word?

i.) PERMUTATION = 11!/2!= 19,1958,400

     PERMUTATION = 11! = The total amount of letters.

                                     = 2! = The total amount of the repeated item "T".

ii.) CALCULUS = 8!/2!2!2! = 80,640    = 8!/ 2! x 2! x 2! = 80,640 

      CALCULUS = 8! = That total amount of letters.

                             = 2! = The total amount  of the repeated item "C".

                             = 2! = The total amount  of the repeated item "L".

                             = 2! = The total amount  of the repeated item "U".

This is all we did on Friday! Thank you for reading. 
lol. 

If I get to choose who goes next, I choose ANN BONIFACIO unless someone volunteers. 

Fin.