*scratch*

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consider this as a graph.
Each pupil is a node.
When they've been on a trip, draw an edge between them.
since they can't go on a trip together twice, the total number of edges allowed in the graph is 30 + 29 + 28 + ... + 2 + 1 = (30/2)(30+1) = 15*31 = 465

now each time you choose 8 pupils, you draw edges between each of them, so you add 8 + 7 + ... + 1  = 36 edges.

So, total number of times you can choose 8 pupils is floor (465 / 36) = 12