Brighton drawn at home in FA Cup fourth round
The Baggies were relegated from the Premier League last season but sit fourth in the Championship this season, five points behind leaders Leeds.
The game will take place over the weekend of January 25 to 28, with the winners receiving £180,000 prize money.
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Hide AdBrighton reached the fourth round on Saturday when goals from Anthony Knockaert, Yves Bissouma and Florin Andone clinched a 3-1 win at Bournemouth.
The Seagulls reached the quarter-finals last year, before going out 2-0 away to Manchester United.
The full fourth round draw is:
Swansea City vs Gillingham
AFC Wimbledon vs West Ham
Shrewsbury or Stoke vs Wolves
Millwall vs Everton
Brighton vs West Brom
Bristol City vs Bolton
Accrington vs Derby or Southampton
Doncaster Rovers vs Oldham
Chelsea vs Sheffield Weds or Luton
Newcastle or Blackburn vs Watford
Middlesbrough vs Newport
Manchester City vs Burnley
Barnet vs Brentford
Portsmouth vs QPR
Arsenal vs Manchester United
Crystal Palace vs Tottenham
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