In Report.cshtml update the "Department" field to use a drop down list.

@model IssueReporter.Models.Issue

@{
    ViewBag.Title = "Report an Issue";
}

<h2>@ViewBag.Title</h2>

@using (Html.BeginForm())
{
    <div>
        @Html.LabelFor(m => m.Name)
        @Html.TextBoxFor(m => m.Name)
    </div>

    <div>
        @Html.LabelFor(m => m.Email)
        @Html.TextBoxFor(m => m.Email)
    </div>

    <div>
      // replaced TextBox with DropDownList
      // added DepartmentSelectedListItems as a second parameterIn 
        @Html.LabelFor(m => m.DepartmentId)
        @Html.DropDownListFor(m => m.DepartmentId, DepartmentsSelectListItems )
    </div>

    <div>
        @Html.LabelFor(m => m.Severity)
        @Html.TextBoxFor(m => m.Severity)
    </div>

    <div>
        @Html.LabelFor(m => m.Reproducible)
        @Html.TextBoxFor(m => m.Reproducible)
    </div>

    <div>
        @Html.LabelFor(m => m.DescriptionOfProblem)
        @Html.TextAreaFor(m => m.DescriptionOfProblem)
    </div>

    <button type="submit">Save</button>
}