Question: three methods for marking animals for mark and recapture sampling

title: Mark and recapture
text: var ⁡ ( N ^ C ) = ( K + 1 ) ( n + 1 ) ( K − k ) ( n − k ) ( k + 1 ) ( k + 1 ) ( k + 2 ) . ( \ displaystyle \ operatorname ( var ) ( ( \ hat ( N ) ) _ ( C ) ) = ( \ frac ( ( K + 1 ) ( n + 1 ) ( K-k ) ( n-k ) ) ( ( k + 1 ) ( k + 1 ) ( k + 2 ) ) ) . )