为了解决以下数据库问题，要编写的查询语句是什么？

I have the following 3 tables in the database.

1. Programs_Table
   Program_ID (Primary Key)
   Start_Date
   End_Date
   IsCompleted
   IsGoalsMet
   Program_type_ID

2. Programs_Type_Table(different types of programs, supports a dropdown list in the form)
   Program_type_ID (Primary Key)
   Program_name
   Program_description

3. Client_Program_Table
   Client_ID (primary key)
   Program_ID (primary key)

What is the best way to find out how many clients are in a specific program (program type)?

Would the following SQL statement be the best way, or even plausible?

SELECT Client_ID FROM Client_Program_Table
INNER JOIN Programs_Table 
ON Client_Program_Table.Program_ID = Programs_Table.Program_ID
WHERE Programs_Table.Program_type_ID = "x"

where "x" is the Program_type_ID of the specific program we're interested in.

OR is the following a better way?

$result = mysql_query("SELECT Program_ID FROM Programs_Table 
WHERE Program_type_ID = 'x'");
$row = mysql_fetch_assoc($result);
$ProgramID = $row['Program_ID'];
$result = mysql_query("SELECT * FROM Client_Program_Table
WHERE Program_ID = '$ProgramID'");
mysql_num_rows($result) // returns how many rows of clients we pulled. 

Thank you in advance, please excuse my inexperience and any mistakes that I've made.

Here is how you can do it:

<?php
// always initialize a variable
$number_of_clients = 0;

// escape the string which will go in an SQL query 
// to protect yourself from SQL injection
$program_type_id = mysql_real_escape_string('x');

// build a query, which will count how many clients 
// belong to that program and put the value on the temporary colum "num_clients"
$query =   "SELECT COUNT(*) `num_clients` FROM `Client_Program_Table` `cpt`
            INNER JOIN `Programs_Table` `pt`
            ON `cpt`.`Program_ID` = `pt`.`Program_ID`
            AND `pt`.`Program_type_ID` = '$program_type_id'";
// execute the query
$result = mysql_query($query);

// check if the query executed correctly 
// and returned at least a record
if(is_resource($result) && mysql_num_rows($result) > 0){
    // turn the query result into an associative array
    $row = mysql_fetch_assoc($result);

    // get the value of the "num_clients" temporary created column
    // and typecast it to an intiger so you can always be safe to use it later on
    $number_of_clients = (int) $row['num_clients'];
} else{

    // query did not return a record, so we have no clients on that program
    $number_of_clients = 0;
}
?>

This returns a count of the clients in a specific program type (x):

SELECT COUNT(cpt.Client_ID), cpt.Program_ID
FROM Client_Program_Table cpt
INNER JOIN Programs_Table pt ON cpt.Program_ID=pt.Program_ID
WHERE pt.Program_type_ID = "x"
GROUP BY cpt.Program_ID

If you want to know how many clients are involved in a program, you'd rather want to use COUNT( * ). MySQL (with MyISAM) and SQL Server have a fast way to retrieve the total number of lines. Using a SELECT(*), then mysql_num_rows leads to unnecessary memory ressources and computing time. To me, this is the fastest, though not the "cleanest" way to write the query you want:

SELECT
    COUNT(*)
FROM
    Client_Program_Table
WHERE
    Program_ID IN
    (
        SELECT
             Program_ID
        FROM
             Programs_Table
        WHERE
             Program_type_ID = 'azerty'
    )

Why is that?

Using JOIN make queries more readable, but subqueries often prove to be computed faster.