If the number of selections of r as well as (n+r) things from 5n different things are equal, then what is the value of r ?

Step-by-step solution

The number of selections of r things from 5n different things is given by ^ 5n C_ r . The number of selections of (n+r) things from 5n different things is given by ^ 5n C_ n+r . Given that ^ 5n C_ r = ^ 5n C_ n+r . Using the property of combinations, if ^ N C_ x = ^ N C_ y , then either x = y or x + y = N . Since r n+r (for n 0 ), we must have: r + (n+r) = 5n 2r + n = 5n 2r = 4n r = 2n Answer: 2n