LONDON - Britain's Prince William and his wife Kate are expecting a third child, their office said on Monday."Their Royal Highnesses The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting their third child," Kensington Palace said in a statement."The Queen and members of both families are delighted with the news," it said.Kate was suffering from extreme morning sickness, a problem which occurred in her two previous pregnancies, and was being cared for at the palace having canceled her official engagements for Monday, the statement said.William and Kate's two children George and Charlotte are aged four and two. Their third child would be fifth in line to the British throne. William, 35, is the eldest son of Prince Charles, the first in line to the throne, and a grandson of the queen.