place 20 chess pieces on a checkerboard, in random places

using System;
using System.Linq;

Piece[] board = whatever();

// New random number generator.
Random random = new Random();

// LINQ query orders each element by the next random number.
Piece[] randomBoard = (from piece in board
    orderby random.Next()
    select piece).ToArray();

int index = (y * 8) + x;

Piece[] pieces = ... your 20 pieces here
Piece[] board = new Piece[8 * 8];
Random r = new Random();
foreach (Piece piece in pieces)
{
    while (true)
    {
        Int32 location = r.Next(board.Length);
        if (board[location] == null)
        {
            board[location] = piece;
            break;
        }
    }
}