Credit: Erin Stevenson O'Connor
Here is a problem from i-want-to-study-engineering.org, the website written by Cambridge University Engineering department that helps you to apply for Engineering courses at top universities.
Jane has 5 pairs of socks. The first pair of socks are both red. The second pair of socks are both blue. The third pair of socks are both green. The fourth pair of socks are both yellow. The fifth pair of socks are both white. One sock from each pair is placed in a bag on the left, and the rest are put in a bag on the right.
In each turn, Jane draws one sock at random from each bag and folds them together to form a pair. After five turns, she has formed 5 pairs of socks. Find the probability that no pair consists of socks of the same colour.