Pita has 12 coins in her bag there are three 1 pound coins and nine 50p coins she takes 3 coins out of the bag at random, work out the probability she takes out exactly £2.50

Let's find the number of 1 pound coins and 50 pence coins that yield us 2.50 pounds.
Let x = number of 1 pound coins
y = number of 50 pence coins

Then 1x + 0.50y = 2.50
and x + y = 3

From the second equation, we get x = 3 – y.
Then substitute it into the first equation:
1(3 – y) + 0.50y = 2.50
3 – y + 0.50y = 2.50
3 – 0.50y = 2.50
Subtract 3 from both sides:
–0.50y = –0.50
Divide both sides by –0.50:
y = 1
Then x = 3 – 1 = 2
So to make 2.50 pounds, she need to take two 1 pound coins and one 50 pence coin.

Next, we have to find the probability that she takes exactly two 1 pound coins and one 50 pence coin. That should be 

P = (3C2)•(9C1)/(12C3) = 0.1227

So the answer is 0.1227.

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