Question

nC(r-1):nCr:nC(r+1)=3:4:5 find r

Answer 1

Given,
nC(r-1):nCr:nC(r+1)=3:4:5
we know,
nCr/nC(r-1)=n-r+1/r
hence,
nCr/nC(r-1)=4/3
=>n-r+1/r=4/3
=>3n-3r+3=4r
=>3n-7r=-3 ---(1)
Again,
nC(r+1)/nCr=5/4
=>n-(r+1)+1/r+1=5/4
=>n-r-1+1/r+1=5/4
=>n-r/r+1=5/4
=>4n-4r=5r+5
=>4n-9r=5 ---(2)
Now,solving equation (1)&(2)
3n-7r=-3 ×(4)
=>12n-28r=-12 ---(3)
4n-9r=5 ×(3)
=>12n-27r=15 ---(4)
substracting equation (3) - (4)
i.e.,(12n-28r)-(12n-27r)=-12-15
=>12n-28r-12n+27r=-27
=>-r=-27
=>r=27