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The number of ways in which a score of 1...

The number of ways in which a score of 11 can be made from a throw by three persons,each throwing a single die once, is

A

45

B

18

C

27

D

68

Text Solution

Verified by Experts

The correct Answer is:
C
Coefficient of `x^(11)` in `(x+x^(2)+x^(3)+x^(4)+x^(5)+x^(6))^(3)`
=Coefficient of `x^(8)` in
`(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(3)`
=Coefficient of `x^(8)` in `(1-x^(6))^(3)(1-x)^(-3)`
=Coefficient of `x^(8)` in `(1-3x^(6))(1+.^(3)C_(1)x+ . . )`
`=.^(10)C_(2)-3xx.^(4)C_(2)=45-18=27`
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