2 Some of the activities that may be involved in making a cup of tea are listed below. A: Boil water.
B: Put teabag in teapot, pour on boiled water and let tea brew.
C: Get cup from cupboard.
D: Pour tea into cup.
E: Add milk to cup.
F: Add sugar to cup. Activity A must happen before activity B.
Activities B and C must happen before activity D .
Activities E and F cannot happen until after activity C.
Other than that, the activities can happen in any order.

1. Lisa does not take milk or sugar in her tea, so she only needs to use activities \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D . In how many different orders can activities \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D be arranged, subject to the restrictions above?
2. Mick takes milk but no sugar, so he needs to use activities \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }\) and E . Explain carefully why there are exactly nine different orders for these activities, subject to the restrictions above.
3. Find the number of different orders for all six activities, subject to the restrictions above. Explain your reasoning carefully.