Question

If three dice are thrown simultaneously, then the probability of getting a score of 7 is

• A. 5/216
• B. 1/6
• C. 5/72
• D. None of these

Answer 1

Answer: (C)

5/72

Answer 2

$n ( S ) = 6 \times 6 \times 6$

n(5) = The number of solutions of $x + y + z = 7$,

where $1 \leq x \leq 5,1 \leq y \leq 5,1 \leq z \leq 5$= Coefficient of $x ^ { 7 }$ in

$\left( x + x ^ { 2 } + \ldots . + x ^ { 5 } \right) ^ { 3 }$ = Coefficient of $x ^ { 4 }$ in $\left( 1 + x + \ldots . . + x ^ { 4 } \right) ^ { 3 }$

= Coefficient of $\left( \frac { 1 - x ^ { 5 } } { 1 - x } \right) ^ { 3 }$

= Coefficient of $\left( 1 - 3 x ^ { 5 } + 3 x ^ { 10 } - x ^ { 15 } \right) ( 1 - x ) ^ { - 3 }$

= Coefficient of $x ^ { 4 }$ in

$= { } ^ { 6 } C _ { 4 } = \frac { 6 ! } { 4 ! 2 ! } = \frac { 6 \times 5 } { 2 } = 15$.

∴ $p ( E ) = \frac { n ( E ) } { n ( S ) } = \frac { 15 } { 6 \times 6 \times 6 } = \frac { 5 } { 72 }$.