How can I solve this Possible three letter words - php

Question

I want to solve this problem of Possible three letter words
Here is following words. (17 characters)
19920620forestJSR
How many possible ways to make 3 length word with given characters?
Ex: 192, 162, Rer, ….
Rule:
Number 0 is different alpha o. (0 != o)
case-sensitive is available. (R != r)
same character repeat not available. (rr1 : wrong)
Hint:
17 16 15 : wrong
How can I solve this
I am trying with this code
function permute($str,$i,$n) {
if ($i == $n)
print "$str\n";
else {
for ($j = $i; $j < $n; $j++) {
swap($str,$i,$j);
permute($str, $i+1, $n);
swap($str,$i,$j); // backtrack.
}
}
}
function swap(&$str,$i,$j) {
$temp = $str[$i];
$str[$i] = $str[$j];
$str[$j] = $temp;
}
$str='19920620forestJSR';
permute($str,0,strlen($str));
But in output have some error with numeric characters
Output look like (when str=19920620forestJSR)
n���Z��뢿�Yh��fzj+�ȳz��ߍ�ｼo+^��aj�-y�k��m��e�ƭ{�6�ټ�zȧo�h���j���Z�ǫ���������z�a���X�y�����
Output look like (when str=forestJSR)
foresSJtR
foresSJRt
foresStJR
foresStRJ
foresSRtJ
foresSRJt
foresRJSt
foresRJtS

Answer 1

The rules says you need combinations of 3 characters, whithout repeating letters. Your code is generating all combinations for 17 letters. So, the script is looping for millions of possibilities (355,687,428,096,000).
The number of permutations of n distinct objects, taken r at a time is
nPr = n! / (n - r)!
So, for "19920620forestJSR" (14 different letters only), using 3 at a time:
14P3 = 14! / (14 - 3)! = 14! / 11! = (14)(13)(12) = 2184