Hi Kai In the first one, I’d rather say draw lots to decide/determine the order In the other two, I’d use “in the order”.

1. To 'draw lots on . .’ means to decide something by a procedure of drawing lots ie randomly picking out - choosing an item that will determine the winner or loser. The preposition ’on’ is part of the expression 'to draw lots on'. 2. ’On the order of missions' could be one of two things: that the ’order of missions’ is a list of journeys that should be made, or that ’Missions’ is the command and control centre that sends instructions, in which case they have sent you an order to do this. 3. This should read ’in order of preference' or ’in your order of preference' ; this means ’write or enter your preferences in the order that you want them considered. Your first preference is the one you would most like; if this is not possible then your second choice is your next preference, and if neither your first or second choices are possible then you will accept your third choice. 'In order of . .’ refers to a set of something that is listed in some order. It could be ’numerical order' for something that is identified by a number, or date order for something for which the time is relevant. You can see from the above examples that ’in (the) order’ and ’on (the) order’ are expressions that relate to different contexts.