If values of a,b,c is given from the set {1,2,3} where a not equal to b not equal to c, then the probability that b2-4ac>0 is what?

Dear Student,

as a is not equal to b and b is not equal to c.
So we can select a,b,c from set of {1,2,3} such that numbers are not repeated.
So this can be done in 3! ways.

This is the total sample size= 6.
Now to satisfy b-4ac>0

Take b=3, a=1,c=2
32-4×1×29-8=1>0Hence (a,b,c)=(1,3,2) satisfies the conditionlet b=3, a=2,c=1b2-4ac>032-4×1×29-8=1>0thus  (a,b,c)=(2,3,1) satisfies the conditiontake b=222-4×1×34-12<0equation not satisfiedalso check for b=112-4×2×31-24<0Hence only two combination (2,3,1),(1,3,2) satisfy the given condition.Thus favourable cases=2Probability that a,b,c satisfy b2-4ac>0P=26=13

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