Please include workings out

b) The UK national lottery works as follows. You choose six (different) numbers in the range 1 to 49. If all six come up in the draw (in any order) you win the first prize, expected to be around E2m (which could be shared if someone else chooses the six winning numbers). i What is the probability of winning the first prize with a single ticket? i You win a second prize if you get five out of six right, and your final chosen number matches the 'bonus' number in the draw (also in the range 1 to 49). What is the probability of winning a second prize? iii) Calculate the probabilities of winning the third, fourth or fifth prize where the third prize is won by matching five out of 6 numbers, a fourth prize by matching four out of six and a fifth prize by matching three out of six. (18 marks) (Total: 33 marks)