A person is permitted to selected at least one and at most `n` coins from a collection of `(2n+1)` distinct coins. If the total number o ways in which he can select coins is 255, find the value of `ndot`

Explanation

According to the question
`.^(2n+1)C_(1)+ .^(2n+1)C_(2)+..+ .^(2n+1)C_(n)=225`
But, `.^(2n+1)C_(0)+ .^(2n+1)C_(1)+..+ .^(2n+1)C_(n)+ .^(2n+1)C_(n+1)+..+ .^(2n+1)C_(2n+1)`
`=2^(2n+1)`
Now `.^(2n+1)C_(1)= .^(2n+1)C_(2n), .^(2n+1)C_(2)= .^(2n+1)C_(2n-1)`
`.^(2n+1)C_(n)= .^(2n+1)C_(n+1) " etc." " " ("using" .^(n)C_(r )= .^(n)C_(n-r)`
`therefore .^(2n+1)C_(0)+2(.^(2n+1)C_(1)+ .^(2n+1)C_(2)+..+ .^(2n+1)C_(n))+ .^(2n+1)C_(2n+1)`
`=2^(2n+1)`
`implies 1+2(255)+1=2^(2n+1)`
`implies 1+255=2^(2n)`
`implies 2^(2n)=2^(8)`
`implies n=4`