Clay Pigeon ShootersDiscrete Mathematics Level 5
Clay pigeon shooting is the art of shooting at special flying targets, known as clay pigeons or clay targets, with a shotgun. Suppose there are \(10\) clay shooters in a professional competition. Each shooter has equal ability and they all use identical shotguns. One throws \(20\) clay targets simultaneously, each shooter picks a target at random and shoots at it once, all the shooters shooting at the same time. The expected number of targets to get hit is \(N\). Determine the value of \(\lfloor N\rceil\), the nearest integer of \(N\).