SOLUTION: pita has 12 coins in her bag. There are 3 £1 coins and 9 50p coins. She takes 3 coins from the bag at random. Work out the probability that she takes exactly £2.50

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