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Number of Hazardous Combination of UraniumIn a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the rule. So he arranges the uranium stack the way he wanted. What is the number of hazardous combinations of uranium in a stack of 5? a) 3 b) 7 c) 8 d) 10
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Solution :-
we have given that, three cubes of uranium together are hazardous.
For a stack of 5 cubes we have 3 cases :- (of hazardous.)
Case 1):- 3 uranium and 2 lead cubes .
→ when all 3 uranium cubes are together, they can be arranged in = {UUULL} , {LUUUL} and {LLUUU} = 3 ways.
Case 2):- 4 uranium and 1 lead cube.
→ when 4 uranium cubes are together, they can be arranged in = {UUUUL} and {LUUUU} = 2 ways.
Also,
→ If 3 uranium cubes are together then they can be arranged in = {UUULU} and {ULUUU} = 2 ways.
Case 3):- All 5 are uranium cubes .
→ 5 uranium cubes can be arranged in = {UUUUU} = 1 way.
Therefore,
→ Total Number of ways = 3 + (2 + 2) + 1 = 8 ways. (Option C) (Ans.)
Hence, the number of hazardous combinations of uranium in a stack of 5 is 8.
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