By DANICA KIRKA
Associated Press

LONDON (AP) - Prince William and his wife, the Duchess of Cambridge, are expecting their third child, Kensington Palace said Monday.

Kensington Palace made the pregnancy announcement as they said that the former Kate Middleton was not feeling well enough to attend an engagement later in the day. As with her other two pregnancies, the duchess is suffering from Hyperemesis Gravidarum, or acute morning sickness. Kate is being cared for at her Kensington Palace home in London.

"The queen and members of both families are delighted with the news," the palace said in a statement.

William and Kate, both 35, already have two children: Prince George, 4, and Princess Charlotte, 2.

The announcement came at a time when the royal couple is due to mark a milestone in the life of their young family: They are set to send George to school for the first time on Thursday.

Their choice of Thomas's Battersea in south London indicated that the Cambridges were settling into their Kensington Palace apartment, having moved recently from their Norfolk home Anmer Hall.

No details were immediately available about when the third baby is due, but betting agencies were quick to start offering odds on possible names for the soon-to-be-born child in the House of Windsor.

Paddy Power offered 8-to-1 odds on Alice. Also popular was Diana, after Prince William's mother, particularly given the timing of the announcement.

Together with Prince Harry, William and Kate have taken a leading role in marking the 20th anniversary of Diana's death. Last week the royals toured the garden of their Kensington Palace home to remember the princes' mother and celebrate her contributions to their family and to the monarchy.

"Given the recent anniversary, there'll be plenty of interest in the name Diana if the baby is a girl," the agency said.

The royals have said from the time of their engagement that they wanted to have a family - the only question was how many children they wished for. Royal watchers recorded every aside for clues as to what the plans might be.

When asked on a royal tour in Singapore in 2012 about how many children he wanted, William said he was "thinking about having two."

More recently, during a royal tour of Poland, Kate joked about a third child when given a cuddly toy designed to soothe tiny babies.

Kate thanked the well-wisher for the present and turned to William. "We will just have to have more babies," she said laughing.

Kate is the eldest of three siblings, and reportedly had a very happy childhood. William has a younger brother, Prince Harry.

The royal couple can also be seen as following in the footsteps of Queen Elizabeth II and Prince Philip, who have four children.

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