Combinations

[pliant yacht]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
   +close

[frozen rune]

hopefully this is right and enough help but not too much solution, combinatorics is super finnicky but should be straightforward if you're careful

for b) it may be helpful to think of every easy-medium block as one unit
therefore you can set it up as (15H + 1B + 5E + 5EM) or as (15H + 1BM + 6E + 4EM)
for the first one there's 10 easy choices for M1, 9 for M2, 8 for M3...
so it's (15 + 1 + 5 + 5)!*10*9*8*7*6 + (15 + 1 + 6 + 4)!*(#ofplacesforthebonus=5)*10*9*8*7
for c) similarly, it must be (1B + 5EMH + 5E + 10H)
for d)
either last question is easy or not
if last question is not easy, think of picking 10 questions from the 21 to go after each easy (and there are several ways to do that so probably generalize, rather than trying to find them all), and then ordering those 21 units
if last question is easy, 10*(# of ways to pick 9 questions from the 21 to go after each other easy)*(21!) in the same way
(this is obviously the hardest question)
for e) you're picking 9 questions from a pool of 30 and then ordering 10 questions

[rough vapor]

Why is "a" 30? I am genuinely curious.

According to me since the bonus question is fixed, you have 30 questions to arrange in 30 different spots and order does matter so its a permutation, 30P30 which is 30!

[frozen rune]

they said 30!

[rough vapor]

oh my bad, I thought it was an exclamation point 💀