x, y and z are 3 integers ranging 1 to 9 (repetition is not allowed). What will be the probability t

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20 Feb 2013 probability

x, y and z are 3 integers ranging 1 to 9 (repetition is not allowed). What will be the probability that x+y+z/x*y*z < 1.

OPtion

1) 1/84
2) 1/28
3) 3/28
4) 17/84
5) 43/84
6) 59/84
7) 74/84
8) 83/84
9) 1
10) none of these

Solution

Only 1*2*3 = 6 = 1+2+3
For all other triplets a*b*c > a+b+c
total no. of triplets = 9*8*7/3*2*1 = 84

Correct Option: 8 Best Solution (8)