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:5764873648575648None

Solution

## The correct option is C 575648Let 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)2.2≤k≤12. ⇒(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 (1−x6)4(1−x)−4 =Coefficient of x10 in (1−4x6+......)(1−x)−4 =13C10−4×7C4=146. Total ways = (36)2 Hence probability (throws are unequal) =1−14636×36=1−73648=575648

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