After days of political horse-trading the UK finally has a new government and a new Prime Minister, following the resignation of Labour's Gordon Brown on Tuesday evening.

Since last Thursday's general election resulted in a hung parliament, a situation in which none of the political parties has an overall majority, British politicians have been attempting to form a coalition government.

Such a government is comparatively rare in the UK. Indeed this is the first coalition since the Second World War.

The Queen invites the new PM to form a government

So how did it happen?

Last week's general election saw the public vote split amongst the political parties in such a way that no party achieved the 326 seatsrequired to gain a majority and therefore form a government.

This situation is known as a hung parliament, and means that two or more of the opposing parties have to unite in order to have more than 326 seats between them.

The Conservative party won 306 seats while Labour and the Liberal Democrats got 258 and 57 seats respectively.

This meant that the Liberal Democrats effectively became 'kingmakers', with the power to choose which rival to form a coalition with.

Both Labour and the Conservatives attempted to woo the Lib Dems with various offers over the last few days, but in the end Gordon Brown resigned both as Prime Minster and as Labour leader, paving the way for the new government.

Many have seen the Lib Dems as the real winners in this situation, given the fact that their leader Nick Clegg has been appointed Deputy Prime Minister and four others have received ministerial appointments.

However, it remains to be seen how effectively David Cameron's Conservatives can work with their new partners.