Permutation and Combination

Blaise Pascal (1623-1662), France mathematician and physician who give contributing mean in theory of probability (possibility because trying to answer in around gambling). The end of his life, he’s thinking religion. One of his idea is that trust to God more sensible because though cannot be proved, trust to God give more advantage of mind.

Permutation and combination in mathematics is complication of certain objects or elements. In combination, sequence of compilation of number not paid attention. But in permutation, reckoned different sequence. Combination and permutation play role important in many mathematics branch.

For example in theory of probability and statistic this theory is used to count the number of compilation which possible from a system. So called new mathematics branch of combinatorica created from bases permutation and combination and have important application and design and operational computer and also other social and physics

For example, in my friend birthday party there is 10 person who attend, everyone is shaking hand each other with other person so everyone shaking hand with 9 person. How many shaking hand that happened in birthday party?

Permutation

The number of permutation who made from n element who different is n!. In 3 element which not all same can made permutation:

P_{α,β,ϒ,.....(n)} =

A way to choice element k from a gathering which consist of  element n with bothering its sequence.

Example:

1.       Calculate permutation from Anton, Rina, and Eko!

Answer:

Amount of permutation from 3 different element (no same element) equal P (3)= 3!= 6

2.       Siti will send letter to her brother from medan and expense of stamp Rp.3000,-. She bought 4 stamp one price Rp.1500,- one again Rp.750,- and rest Rp.500,- and Rp.250,-.

Answer:

(back to no same element) P (n)= P (4)= 4!= 24.

3.       A Permutation sequence from word of KATAKAN is....

Answer:

Word of KATAKAN compose from 4 different letter are K, A, T, and N. K emerge 2 times, A 3 times, T and N 1 time. Amount of letter is 7 so that permutation is

So there is 420 probabi lity sequence of letter which different with attention sequence. For example KATAKAN different with NAKATAK.

Combination

A way to choice element k from a gathering which consist of  element n without bothering its sequence.

Example, there 4 person name is Dewi, Doddy, Medria, and Hendradi. How many choice if we will choice 2 person?

Answer:

= 6