Question

Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is k

(9 £ k £ 14), is -

• A.
• B. $\frac { \mathrm { k } ^ { 2 } - 3 \mathrm { k } + 2 } { 432 }$
• C.
• D. None of these

Answer 1

Answer: (A)

Answer 2

Favourable number of elementary events

= Coeff. of x^k–3 in (1 – x⁶)³ (1 – x)^–3

= Coeff. of x^k–3 in (1 – ³C₁x⁶ + …) (1 – x)^–3 [Q 9 £ k £ 14, \ 6 £ k – 3 £ 11]

= Coeff. of x^{k – 3} in (1 – x)^–3 – ³C₁ (Coeff. of x^{k – 9} in (1 – x)^–3)

= ^k–3+3–1C_3–1 – ³C₁ × ^k–9+3–1C_3–1

= ^k–1C₂ – 3. ^k–7C₂

= – 3. = 21k – k² – 83. The total number of elementary events associated to the random experiment of throwing three dice is 6 × 6 × 6 = 6³.

Hence, the probability of the required event

= Hence, (1) is correct answer