Question
In how many ways can we get a sum of at most 17 by throwing six distinct dice -
- 6940
- 7881
- 9604
- None of these
The correct answer is: 9604
x1 + x2 + x3 + x4 + x5 + x6 17
When 1 
xi 6, i = 1, 2, 3, …..6
Let x7 be a variable such that
x1 + x2 + x3 + x4 + x5 + x6 + x7 = 17
Clearly x7 
0 Required number of ways
= Coefficient of x17 in (x1 + x2 + ….. + x6)6
(1 + x + x2 + …..)
= Coefficient of x11 in 
= Coefficient of x11 in (1– 6C1 x6 + 6C2 x12……) (1 – x)–7
= Coefficient of x11 in (1 – x)–7 – 6C1 × coefficient of x5 in (1 – x)–7
= 11+7–1C7–1 – 6C1 × 7+5–1C7–1
= 17C6 – 6 × 11C6 = 9604.
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