G8-develop and apply formulas to evaluate permutations and combinations

Originators: Dylan and Matt

To develop a formula for a permutation or a combination first you must decide which of the 2 you are dealing with.

-With a combination order dosent [doesn't]  matter so if you are to choose 3 people for 3 of the exact same jobs then it does not matter who you choose for the first slot, who you choose for the second slot and who you choose for the third slot.

                3C3=1

-With a permutation order does matter so if you are to choose 3 people, 1 for president, 1 for vice president and 1 for secretary it does matter who you choose for a position. There is [are] many more options.

               3P3=6

Deriving a formula for combinations: (nCr) to make the formula you take the the number of total objects(n) factorialed and divide by the chosen number of objects(r) factorialed and multiply by the total number(n) minus the chosen number(r) factorialed.

nCr= n!/r!(n-r)!

Say you have 6 students and need to choose 3 of them for a debate team where one position is no different then the other you would apply as shown below:

6C3= 6!/3!(6-3)!= 20

Deriving a formula for permutations: (nPr) to make the formula you take the number of total objects (n) factorialed and divide by the the total number of objects (n) subtract the chosen number of objects (k) factorialed.

nPr= n!/(n-k)!  [I think you mean (n-r)! for the denominator]

Say you have 6 students and you need to choose 3 for a debate team where 1 student is the opener, 1 student is the body of the debate and the last is the conclusion. You would apply as shown below:

6P3= 6!/(6-3)!= 120