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3.LetX={m,m+1,···,n 1,n}beasetofconsecutivepositiveintegers,andA
thesubsetofXconsistingofthoseelementswhicharemultiplesof3.Youwouldexpect|A|tobeabout|X|
3
n .(b)ShowthatifX={1,2,···,n},then|A|=
2 + n
23 + n
=0.)2k
(c)Deducethatv2((2n)!)=n+v2(n!).Howcouldthisbeprovedanotherway?*5.LetFnbethesetoffunctionsf:{1,2,...,n}→{1,2,...,n}suchthatifi<j
thenf(i) f(j),andforalli,f(i) i.Giventworowsofboxeswithnboxesineachrow,
...
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