9 distinct balls are distributed among 4 boxes B_1,,B_4.

Question

9 distinct balls are distributed among 4 boxes $B_1,\dots,B_4$. If $P(B_3	ext{ has exactly 3 balls})=\dfrac{k}{3^4}\cdot\dfrac{1}{9}$ (per source: $=k\cdot\dfrac{3^9}{4^9}$ form), $k$ lies in the set:

Accepted Answer

$$P = \frac{{}^9C_3\cdot3^6}{4^9}$$

Comparing with the given form $k\cdot\dfrac{3^9}{4^9}$: $k=\dfrac{{}^9C_3}{3^3}=\dfrac{84}{27}\approx3.11$, which satisfies $|x-3|<1$.

Solutions · 1