If  nPr=1680 and  nCr=70 then n is equal to

nPr=(r!) nCr⇒1680=(r!)(70)⇒r!=24⇒r=4Also 1680=nP4=n(n−1)(n−2)(n−3)⇒n2−3nn2−3n+2=1680⇒n2−3n+12=412⇒n2−3n+1=41⇒n2−3n−40=0⇒(n+5)(n−8)=0⇒n=8.