# Let y be an element of the set A={1,2,3,4,5,6,10,15,30} and x_(1), x_(2), x_(3) be integers such that x_(1)x_(2)x_(3)=y, then the number o

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Let y be an element of the set A={1,2,3,4,5,6,10,15,30} and x_(1), x_(2), x_(3) be integers such that x_(1)x_(2)x_(3)=y, then the number of positive integral solutions of x_(1)x_(2)x_(3)=y is
A. 81
B. 64
C. 72
D. 90

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(b) Number of solutions of the equation x_(1)x_(2)x_(3)=y is the same as the number of solutions of equation
x_(1)x_(2)x_(3)x_(4)=30=2xx3xx5
where x_(4) is dummy variable
Now number of solutions = number of ways distinct integers 2, 3 and 5 can be distributed in four boxes x_(1),x_(2),x_(3) and x_(4)=4^(3)=64