She must have 2 £1 coins and 1 50p coin.

She can choose the 2 £1 coins 3C2 = 3 ways.

For each of those 3 ways she can choose the
50p coin 9C1 or 9 ways.

That's 3×9=27 ways to get £2.50.

She can choose any 3 coins in 12C3 = 220 ways.

The desired probability is 27 ways out of 
220 ways,

or 27/220, or 13.5% of the time.

Edwin