A factory produces chocolates in three flavours: lemon, orange, and strawberry in the ratio 3:5:7 respectively. Nell checks the chocolates on the production line by choosing chocolates randomly one at a time.

1. (a) Find the probability that the first chocolate with lemon flavour that Nell chooses is the 7th chocolate that she checks.
2. (b) Find the probability that the first chocolate with lemon flavour that Nell chooses is after she has checked at least 6 chocolates.

‘Surprise’ boxes of chocolates each contain 15 chocolates: 3 are lemon, 5 are orange, and 7 are strawberry. Petra has a box of Surprise chocolates. She chooses 3 chocolates at random from the box. She eats each chocolate before choosing the next one.

3. (c) Find the probability that none of Petra’s 3 chocolates has orange flavour.
4. (d) Find the probability that each of Petra’s 3 chocolates has a different flavour.
5. (e) Find the probability that at least 2 of Petra’s 3 chocolates have strawberry flavour given that none of them has orange flavour.