MySQL not recognising datetime index in WHERE - mysql

Question

What I'm trying to do is index the first name of a person and the date they were born.
The table is laid out like this:
CREATE TABLE test
(
id INT NOT NULL AUTO_INCREMENT,
fname VARCHAR(10) NOT NULL,
sname VARCHAR(10) NOT NULL,
age INT NOT NULL,
born DATETIME NOT NULL,
PRIMARY KEY(id),
INDEX name_age(fname, sname, age),
INDEX name_date(fname, born)
)
However the index isn't recognised in a where statement like so:
mysql> EXPLAIN SELECT *
-> FROM `test`
-> WHERE fname = "coby"
-> AND born
-> BETWEEN "1900-05-02 06:23:00"
-> AND "2100-05-02 06:23:00";
+----+-------------+-------+------+--------------------+----------+---------+-------+------+-------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+------+--------------------+----------+---------+-------+------+-------------+
| 1 | SIMPLE | test | ref | name_age,name_date | name_age | 12 | const | 45 | Using where |
+----+-------------+-------+------+--------------------+----------+---------+-------+------+-------------+
1 row in set (0.00 sec)
However it is recognised in an order by statement:
mysql> EXPLAIN SELECT *
-> FROM `test`
-> WHERE fname = "coby"
-> ORDER BY born;
+----+-------------+-------+------+--------------------+-----------+---------+-------+------+-------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+------+--------------------+-----------+---------+-------+------+-------------+
| 1 | SIMPLE | test | ref | name_age,name_date | name_date | 12 | const | 45 | Using where |
+----+-------------+-------+------+--------------------+-----------+---------+-------+------+-------------+
1 row in set (0.00 sec)
How do I make it so that the index is recognised in a where statement?
Any help would be appreciated.

Answer 1

The index is recognized, as seen in the column possible_keys of the result of the first EXPLAIN statement. It just happens, that for 45 rows the other index produces an equal or better query plan: The selectivity of your date range is close to zero.
The ORDER BY is another pair of shoes: As you use the index not only for selection, but also for ordering, it now becomes useful.