Generate mathematical combinations with PHP array

Question

GENERATE all possible combinations of 15 elements from an array of 17 items. This is a hypothetical situation. Should serve for any combination n per p.

A total of 136 combinations. Using the Mathematical Formula for Combinations:

Cn,p
C17,15 = 17!/(15!*2!)

???? how to do it? suggestions, examples?

//Código

//array com 17 dezenas

dezenas = ["2", "4", "5", "6", "7", "9", "10", "12", "15", "16", "18", "20", "21", "22", "23", "24", "25"];

//Gerar todas combinações possíveis de array com 15 dezenas

 array1 = ["2", "4", "5", "6", "7", "9", "10", "12", "15", "16", "18", "20", "21", "22", "23"];

 array2 = ["2", "4", "5", "6", "7", "9", "10", "12", "15", "16", "18", "20", "21", "22", "24"];

//etc... etc...

Answer 1

Combinations of 17 elements from 15 to 15 can be defined recursively using the following function:

$dezenas = array("2", "4", "5", "6", "7", "9", "10", "12", "15", "16", "18", "20", "21", "22", "23", "24", "25");

function combinacoesDe($k, $xs){
     if ($k === 0)
         return array(array());
     if (count($xs) === 0)
         return array();
     $x = $xs[0];
     $xs1 = array_slice($xs,1,count($xs)-1);
     $res1 = combinacoesDe($k-1,$xs1);
     for ($i = 0; $i < count($res1); $i++) {
         array_splice($res1[$i], 0, 0, $x);
     }
     $res2 = combinacoesDe($k,$xs1);
     return array_merge($res1, $res2);
}


print_r(combinacoesDe(15,$dezenas));

Result - ideone

From PHP 5.4 you can also use the contracted array syntax, which you exchange array() for [].

Link to generate online combination Online Calculator: Combinatorics. Generator of Combinations

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The number of combinations is given by the formula

                 n!
      Cn,p = ___________     
             p! (n – p)!

• n is the quantity of elements of a set
• p is a natural number less than or equal to n, representing the amount of elements that will form the groupings.

Making the bill without calculating machine we will have :)

                 17!
     C17,15 = ____________     
             15! (17 – 15)!


               (1*2*3*.......*15)*16*17     16*17
     C17,15 =  _________________________ = ______ = 8*17= 8*(10+7)=80+56=136
               (1*2*3*.......*15)*1*2        1*2