Question

A standard card deck consists of 52 cards, divided into four groups of 13 cards (called suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)). In each suit, the cards have 13 different "faces": A,2,3,4,5,6,7,8,9,10, J, Q, K. (a) in how many ways can I select five cards from the deck? (b) in how many ways can I select five cards from the deck, if all cards must belong to the same suit? (c) in how many ways can I select five cards from the deck, if four cards must have same face? 2) A binary mxn matrix is a matrix with m rows and n columns, whose entries can be only 0 or 1. How many mxn binary matrices are there? 3) A computer lab has 25 computers. We have 17 Ethernet cables, and would like to use these cables to connect some of the computers in the lab (assume that each computer can be connected to many computers at once). In how many ways can I do that? 4) A set S has n elements. In how many ways can I select two subsets A,B of S that are disjoint? Find a formula (try small sets first)

Answer 1

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