$10$ questions selected from a bank of $25$ questions. Easiest question first and hardest question always last. # of different ways.

Question

$10$ questions selected from a bank of $25$ questions. Easiest question first and hardest question always last. # of different ways?

I calculated the number of ways with no conditions was $11861676288000$.

How do I calculate if the easiest question is first and hardest question is last?

Answer 1

The question is ambiguous as to whether the easiest and hardest questions refer to the whole bank or only the selection.

If they refer to the selection, then after choosing the ten questions ($\binom{25}{10}$ ways) and fixing the easiest and hardest questions, there remain 8 questions permutable in $8!$ ways. This gives $\binom{25}{10}×8!=131796403200$ ways.

If they refer to the whole bank, there are only 23 questions to choose 8 questions from, leading to $\binom{23}8×8!=19769460480$ ways.