CISC 102 Lecture Notes - Lecture 29: Complex Instruction Set Computing, Bijection, Binomial Coefficient

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Suppose we have a peculiar deck of cards so that suits are omitted (clubs, diamonds, hearts, spades). We have 4 identical aces, 4 identical 2s, so on, up to 4 identical kings. There are 52! ways to shuffle 52 distinct cards. However, there are 4 cards of each value so the num of distinguishable ways to shuffle these cards is: Pick a box of 10 timbits and choose as many as you like from the choice of. The way to model this is to consider a bag w balls labelled c, s, p, g and we count the num of ways to select 10 without ordering and with replacement. It appears that the existing methods do not solve this counting problem very easily. Consider the following seemingly unrelated problem, that of counting the number of binary strings of length 13, consisting of 10 0"s and 3 1"s. We can count the total number of this type of string as.

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