if ⁿC_r - 1 = 36,ⁿC_r = 84 and ⁿC_r+1 = 126, then find ^rC₂.

[HINT : form eqn using ⁿCr/ⁿC_r+1 and ⁿC_r/ⁿC_r-1 to find the value of r.]

ⁿC _r / ⁿC_r+1 = r+1 / n-r =84/126 =2/3

r+1 / n-r =2/3 , 3r+3=2n-2r , ( 2n-5r-3=0 )x 3 = 6n-15r-9=0 .......(i)

ⁿC_r/ⁿC_r-1 =n-r+1 / r =84/36 =7/3

n-r+1 / r = 7/3 ,,, 3n-3r+3=7r, (3n-10r+3=0) x2 = 6n-20r+6=0.......(II)

from i - ii , we have r=3

therefore, ^rC₂ = ³C₂ = 3