If `""^(56)P_((r+6)):""^(54)P_((r+3))=30800:1`, find r.

Explanation

`""^(56)P_((r+6)):""^(54)P_((r+3))=30800:1`
`rArr((56)!)/((56-(r+6))!)xx(((54)-(r+3))!)/((54)!)=(30800)/(1)`
`rArr((56)!)/((50-r)!)((51-r)!)/((54)!)=30800`
`rArr(56)(55)(51-r)=30800`
`rArr(51-r)=(30800)/(56xx55)=10`
`rArrr=41`
It can be verified that r =41 satisfies the given equation.