Don't try to make tired yourself 3

$a_6$ can be $5,6,7,8,9,10$

When $a_6=5$ there are $\binom{5}{5}=1$ possibilities are there for $a_1,a_2,...,a_5$

When $a_6=6$ there are $\binom{6}{5}=6$ possibilities are there for $a_1,a_2,...,a_5$

When $a_6=7$ there are $\binom{7}{5}=21$ possibilities are there for $a_1,a_2,...,a_5$

When $a_6=8$ there are $\binom{8}{5}=56$ possibilities are there for $a_1,a_2,...,a_5$

When $a_6=9$ there are $\binom{9}{5}=126$ possibilities are there for $a_1,a_2,...,a_5$

When $a_6=10$ there are $\binom{10}{5}=252$ possibilities are there for $a_1,a_2,...,a_5$

Total number of selection $462$

In any tuples $a_1 \to a_5$ can arrange in $5!=120$ ways as they are distinct

So, number of ordered pairs are $120 \times 462=55440$