Question

If `.^(n)C_(r-1)=36, .^(n)C_(r)=84 and .^(n)C_(r+1)=126`, find n and r.

Answer 1

Correct Answer - n=9, r=3
`(.^(n)C_(r-1))/(.^(n)C_(r))=(r)/(n-r+1) and (.^(n)C_(r))/(.^(n)C_(r+1))=(r+1)/(n-r)`.
`:. (r)/(n-r+1)=(36)/(84)=(3)/(7)rArr 3n-3r+3=7r rArr3n-10r=-3 " " ...(i)`
and `(r+1)/(n-r)=(84)/(126)=(2)/(3)rArr 2n-2r=3r+3rArr 2n-5r=3. " " ...(ii)`