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Question Number 47481 by limite last updated on 10/Nov/18
Threesix−faceddicearethrowntogether.Theprobabilitythatthesumofthenumbersappearingonthediceisk(3⩽k⩽8)is
Answered by ajfour last updated on 10/Nov/18
coeff.ofx3+coeff.ofx4+.......+coeff.ofx8intheexpansionof(x+x2+x3+x4+x5+x6)3beNP(k)=N216.(x+x2+x3+x4+x5+x6)3=x3(1−x6)3(1−x)3=x3(1−3x6+...)(1−x)−3N=coeff.ofxkwhere3⩽k⩽8is=coeff.ofxk−3intheexpansionof(1−x)−3=Σ3+k−3−1C3−1=Σk−1C2=7C2+6C2+5C2+4C2+3C2+2C2=21+15+10+6+3+1=56P(k)=56216=727.
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