School moving out (Day 1)
Brachylog, 4 bytes

It's always nice to see a challenge and know brachylog is gonna beat everyone.
Takes current classes as input and new classrooms as output; It will output true if it finds a way to fit the students, false otherwise

p≤ᵐ⊆


Explanation

The code has 3 parts of which the order actually doesn't matter

≤ᵐ --&gt; projects each value to a value bigger/equal then input
⊆  --&gt; input is a ordered subsequence of output
p  --&gt; permutes the list so it becomes a unordered subsequence


Try it online!