Remove SharePoint 2010 library authorization using powershell?

Question

I know it's possible to modify a library authorizations using the SharePoint UI following the steps bellow:

1. Stop authorizations inheritance.

2. Modify users authorizations.

3. Select/Unselect the desired checkboxes.

4. OK.

I want to add Reader authorization and remove Contributor.

How to achieve that using PowerShell?

So far, I succeeded to add new authorizations with PowerShell. Here is the code.

$web = Get-SPWeb "http://www.whatever";         
$list = $web.Lists["MyList"];
$list.BreakRoleInheritance($true,$true);    
$group = $web.Groups["Members of the site"];                
$roleToAdd = "Reader";
$role = $web.RoleDefinitions | where {$_.Type -eq $roleToAdd};                      
$assignment = New-Object Microsoft.SharePoint.SPRoleAssignment($group);         
$assignment.RoleDefinitionBindings.Add($role);          
$list.RoleAssignments.Add($assignment); // How to remove instead ?
$list.Update();     
$web.Dispose();

Note: I do know that at least one authorization should be selected.

A solution could be to use this method. Unfortunately it's not working.

$roleToLet = "Reader"
$role = $web.RoleDefinitions | where {$_.Type -eq roleToLet };                      
$assignment = New-Object Microsoft.SharePoint.SPRoleAssignment($group);         
$list.RoleAssignments[1].ImportRoleDefinitionBindings($assignment.RoleDefinitionBindings);
$list.Update();

Answer 1

The list assignments are obtained using the wrong method. Moreover, the assignments were not updated after modifications. Finally I used $web.SiteGroups instead of $web.Groups. It should be as following:

$group = $web.SiteGroups["Members of the site"];
$rolesToRemove = "Contributor";
$role = $web.RoleDefinitions | where {$_.Type -eq $rolesToRemove};                      
$assignment = list.RoleAssignments.GetAssignmentByPrincipal($group);
$assignment.RoleDefinitionBindings.Remove($role);
$assignment.update();                                                       
$list.Update();