![]() ![]() Row \(n\) is the coefficients of the expansion of \((x+y)^n\). ![]() The pattern holds for any \(n\) and \(r\): there are \(n\) ways to choose the first item, \(n-1\) for the second, and so on. ![]() We found the number of 5-permutations of the 52 cards earlier: \(52\cdot 51\cdot 50\cdot 49\cdot 48\).Obviously these are integers with \(0\le r \le n\).We will write \(P(n,r)\) for the number of \(r\)-permutations of \(n\) elements.(“How many permutations are there of these 6 things?” is asking about 6-permutations.) If we don't specify an \(r\), then we mean all of the elements.“too” is not a permutation of those values, since one element is included twice.these are different 3-permutations of the 26 lowercase letters: “ate”, “fog”, “ear”, “wqx”. An \(r\)-permutation is a selection of \(r\) objects.A permutation is a selection of objects in a particular order.For the second question, A wins, then B, then C is a different outcome than B then C then A. ![]()
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