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Question

Let x+y=20, x,yW, the set of non-negative integers. If S is the maximum value of xy and the probability of xy not less than 3S4 is nm, where m and n are co-prime, then the value of n+m is

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Solution

Given x+y=20
The maximum value of xy is when x=y=10,
S=10×10=1003S4=75

Now, xy75
x(20x)7520xx275x220x+750(x5)(x15)0x[5,15]
Required number of values of x is 11
Total number of possible values of x is 20
Therefore, the required probability =1120
nm=1120n+m=31

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