(a) You discover that your school notebook has only k = 6 sheets of paper left i

Question

(a) You discover that your school notebook has only k = 6 sheets of paper left in it. You are attending n = 3 different classes today: Archaeology (A), Buddhism (B), and Computer Science (C). How many ways are there to allocate your six sheets of paper across your three classes so that each class has at least one page for notes? (No paper splitting or hoarding: each sheet must be allocated to one and only one class!)

(b) Consider a computer network with 60 switching nodes. The network is designed to withstand the failure of any two nodes.

i. In how many ways can one or two nodes fail?

ii. In how many ways can a failure of network occur?

iii. If one node has failed, in how many ways can seven nodes be selected without encountering the failed node?

iv. If two nodes have failed, in how many ways can seven nodes be selected to include exactly one failed node?

Explanation / Answer

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