### Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

### Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

### Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

# CD Collection

##### Age 14 to 16 Short Challenge Level:

First, we need to decide which artist will go first, which will go second, and which will go third.

There are 3 options for the artist that goes first, and then 2 options remaining for the artist that goes second, and then only 1 option left for the artist that goes third. So there are 3$\times$2$\times$1 = 6 ways to decide which artist will go first, which will go second, and which will go third.

There are 2 Beatles CDs, so for each position that they could be in relative to the other CDs, there are 2 options for the Beatles CDs - because they could go either way round.

Similarly, since there are 3 Elvis Presley CDs, for each position that they could be in relative to the other CDs, there are 3 options for the first Elvis Presley CD, 2 options for the second and only 1 option for the third. So there are 3$\times$2$\times$1 = 6 ways to arrange the Elvis Presley CDs.

So altogether, there are 6$\times$2$\times$6 = 72 ways to arrange the CDs.
You can find more short problems, arranged by curriculum topic, in our short problems collection.