Integral solutions
Find the number of positive integral solutions for a , b , c such that a b c = 4 5 .
The answer is 18.
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1 solution
For { 1 , 1 , 4 5 } , the number of permutations isn't 3 ! since 1 is repeated twice.
You also left out the case of { 3 , 3 , 5 } in your solution. You got the answer correct but your solution is unjustified and incomplete.
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Yes, you are right. My solution have mistake.
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You can use the "Edit" option to edit your solution and correct the mistake.
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@Prasun Biswas – Yes, I have done it. Thank you.
You have to consider the case ( 3 , 3 , 5 ) who can arrange in 3 ! / 2 = 3 ways. Again, in the same way ( 1 , 1 , 4 5 ) can arrange in 3 ways.
Thus the result follows 6 + 6 + 3 + 3 = 1 8
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Yes, you are right. My solution have mistake.
You should be more specific in your question. What sort of solutions are allowed?
I'm pretty sure you mean 5 * 1 * 9 = 45. You should probably fix that in your solution.
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yes. you are right. I have edited this problem. Thanks... :)
1 , 3 , 15 = 3! = 6
1 , 5 , 9 = 3! = 6
1 , 1 , 45 = ( 3! / 2 ) = 3
3 , 3 , 5 = ( 3! / 2 ) = 3
for example , 1 * 3 * 15 = 45 , 5 * 1 * 9 = 45 , 45 * 1 * 1 = 45 etc.
so answer is , 6 + 6 + 6 = 18 .