How to check if words can be created from list of letters?

I have a string $raw="aabbcdfghmnejaachto" and an array $word_array=array('cat','rat','goat','total','egg').

My program needs to check whether it is possible to make the words in the array with letters from the string. There is one extra condition; if the word contains a letter occurring more than once, that letter must occur at least the same number of times in the string.

E.g. egg. There are two g's. If the string $raw doesn't contain two g's, then it's not possible to make this word.

This is my expected result:

Array([cat]=>'Yes',[rat]=>'No',[goat]=>'Yes',[total]=>'No',[egg]=>'No')

I tried the following, but it doesn't output the expected result:

$res=array();
$raw="aabbcdfghmnejaachto";
$word_array=array('cat','rat','goat','total','egg');
$raw_array= str_split($raw);
foreach($word_array as $word=>$value)
{
    $word_value= str_split($value);
    foreach($word_value as $w=>$w_value)
    {
        foreach($raw_array as $raw=>$raw_value)
        {
            if(strcmp($w_value,$raw_value)==0)
            {
                $res[$value]='Yes';
            }
            else
            {
                $res[$value]='No';
            }
        }
    }
}
print_r($res);

EDIT: The code, as originally posted, was missing the letter e from the string $raw so the egg example would actually return No. I have updated the Question and all the Answers to reflect this. - robinCTS