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Question: Answered & Verified by Expert
If 4 dice are rolled once, the number of ways of getting the sum as 10 is K, then the value of K10 is equal to
MathematicsPermutation CombinationJEE Main
Solution:
2891 Upvotes Verified Answer
The correct answer is: 8
x1+x2+x3+x4=10; 1xi6
The desired number is the coefficient of x10 in
x+x2++x64=x41+x++x54
or the coefficient of x6 in 1+x+x2++x54
=1-x61-x4=1-x641-x-4
=1-4x6+1-x-4
or the coefficient of x6 in 1-x-4-4× coefficient of x0 in 1-x-4
=6+4-1C4-1-4×0+4-1C4-1
=9C3-4×1=9×8×73×2-4=84-4=80
K=80K10=8

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