A company has two plants (A and B) that make a component. Thecompany manufacture
ID: 2918420 • Letter: A
Question
A company has two plants (A and B) that make a component. Thecompany manufacturers a sub-assembly that is made up of three ofthis component part. If Company A supplies five of the componentpart and Company B supplies 3 of the component part, how manydifferent combinations of the sub-assembly containing the threeparts are possible if: a) There are no restrictions on where a part came from (PlantA or Plant B)? b) It is desired to have 2 parts came from Plant A and 1 partcame from Plant B? c) It is desired to have 1 part came from Plant A and 2 partscame from Plant B but a certain part (marked part) from plant B hasto be in the sub-assembly? A company has two plants (A and B) that make a component. Thecompany manufacturers a sub-assembly that is made up of three ofthis component part. If Company A supplies five of the componentpart and Company B supplies 3 of the component part, how manydifferent combinations of the sub-assembly containing the threeparts are possible if: a) There are no restrictions on where a part came from (PlantA or Plant B)? b) It is desired to have 2 parts came from Plant A and 1 partcame from Plant B? c) It is desired to have 1 part came from Plant A and 2 partscame from Plant B but a certain part (marked part) from plant B hasto be in the sub-assembly?Explanation / Answer
This is a problem from counting.
A supplies 5 components and B supplies 3 components
a) When there is no restriction onparts then it is the case of selecting 3 components out of total 8components = 8c3 = 56
b) When we should have 2 from A and 1from B. # Ways to select 2 from A = 5c2 = 10 and # ways ofselecting 1 component from B = 3c1 = 3 . Therefore total number ofways = 10*3 = 30
c) Since the selected part fromB has to come we have choice in only selecting 2 parts .we canselect 1 part form A in 5c1 =5 ways and 1 from the rest 2 parts ofB in 2c1 = 2 ways. Hence total number of ways = 2*5 = 10 ways
HHHope ithelps and feel free to ask for any clarifications.
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