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Question

Two persons each makes a single throw with a pair of dice.  Then  the probability that the sum on both dice are unequal, is:
  1. 57648
  2. 73648
  3. 575648
  4. None


Solution

The correct option is C 575648
Let number of ways for sum of number on two dice for both person will be ak, where 
ak =coefficent of xk in (x+x2+.......+x6)2.2k12.
(x+x2+......+x6)2=a2x2+a3x2+a3x3+.....+a12x12
Then
a22+a23+........+a212= constant term in
(a2x2+a3x3+.......+a12x12)(a2x2+a3x3+......+a12x12)2
=(x+x2+......+x6)2(1x+1x6+.....+1x6)6
=Coefficient of x10 in (1+x+x2+......+x5)4
=Coefficient of x10 in (1x6)4(1x)4
=Coefficient of x10 in (14x6+......)(1x)4
=13C104×7C4=146.
Total ways = (36)2
Hence probability (throws are unequal)
=114636×36=173648=575648

 

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