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# A6

last edited by 13 years, 7 months ago

OUTCOME A6: Develop an understanding of Factorial Notation and apply it to calculating Permutations and Combinations

ORIGINATORS:

Isaac IS A VERY PRETTY FLOWER & Emily IS A VERY PRETTY HAM DEMON

EXPLANATION:

Factorial Notation is you multiply the stated number by its predecessors until you reach one. A Factorial is stated by showing a number followed by an exclamation mark. For example 5! = 5 x 4 x 3 x 2 x 1 = 120. Permutations are, as is explained in outcome G7, expressions of any ordering of a set of numbers (or anything, really), in which order does matter. Combinations are expressions of any ordering of a set of something in which order does not matter. The point of calculating permutations and combinations is to find the number of possible outcomes. To calculate a permutation, you can enter n P r into your calculator, where "n" is the total number of things or numbers available and "r" is the number of places available, OR you can use factorials to solve it using this formula: n P r =   n!

(n-r)!

You can solve combinations by entering n C r into your calculator, or you can use factorials and solve it using this formula: n C r =  n!

n!(n-r)!

SAMPLE PROBLEMS:

The Giant Rabid Mongoose was rampaging across the Earth, when he felt a tad sleepy. He decided that after another six villages, he was going to take a nap. He had 13 villages (Village 1, Village 2, Village 3, Village 4, Village 5, Village 6, Village 7, Village 8, Village 9, Village 10, Village 11, Village 12, and Village 13) to choose from.

a. All of the villages are equidistant from each other, and if you were to bet on the six that he destroyed in the correct order, what would the probability of being correct be?

b. If you were to bet on the six that he destroyed disregarding order, what would the probability of being correct be?

After a long day of utter destruction, GRM is ready to take a lengthy nap.

SOLUTIONS:

a. 13 P 6  =     13!       =  13!   =  13x12x11x10x9x8x7x6x5x4x3x2x1  =  1235520

(13 – 6)!        7!                     7x6x5x4x3x2x1

The probability of getting the correct order would be     1

1235520

b. 13 C 6 =      13!        =   13!      =  6227020800  =  1716

6!(13 – 6)!     (6!)(7!)         3628800

The probability of getting the right numbers would be   1

1716