2. The planner in charge of raw materials operations at a well known beer-producing company needs...

 

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2. The planner in charge of raw materials operations at a well known beer-producing company needs to obtain 5 truckloads of fresh water. The five trucks available can go to any of 11 sources of water (mainly dams and reservoirs). The basic question is how many possible ways this can be achieved. The 11 sources all have different kinds of minerals in the water, so it is always important how many truckloads come from which source, but there are different conditions as follows. Find the number of ways in each case. You may leave your answer expressed in terms of binomials, factorials, integers raised to integer powers, or products and quotients of these, unless otherwise requested. (Important: make sure you explain what formulae you use, and why. (a) It does not matter which truck brings which kind of water, and any sources can be used by any number of trucks. Express your answer as a single integer. (b) It does not matter which truck brings which kind of water, but no source can be used by more than one truck. In this case, give the answer as a single integer. (c) The company needs to keep track of how far each truck goes, so two arrangements are counted as different if they send different trucks to any given source. Still, no source can be used by more than one truck. 2. The planner in charge of raw materials operations at a well known beer-producing company needs to obtain 5 truckloads of fresh water. The five trucks available can go to any of 11 sources of water (mainly dams and reservoirs). The basic question is how many possible ways this can be achieved. The 11 sources all have different kinds of minerals in the water, so it is always important how many truckloads come from which source, but there are different conditions as follows. Find the number of ways in each case. You may leave your answer expressed in terms of binomials, factorials, integers raised to integer powers, or products and quotients of these, unless otherwise requested. (Important: make sure you explain what formulae you use, and why. (a) It does not matter which truck brings which kind of water, and any sources can be used by any number of trucks. Express your answer as a single integer. (b) It does not matter which truck brings which kind of water, but no source can be used by more than one truck. In this case, give the answer as a single integer. (c) The company needs to keep track of how far each truck goes, so two arrangements are counted as different if they send different trucks to any given source. Still, no source can be used by more than one truck.