Question

Six balls are placed randomly into six cells. Then the probability that exactly one cell remains empty is

• A. $\frac{29}{216}$
• B. $\frac{35}{216}$
• C. $\frac{25}{108}$
• D. $\frac{31}{108}$

Answer 1

The correct option is C $\frac{25}{108}$

Six balls can be stored in $6$ cells in $6^6$ ways
For exactly one cell remains empty in that case exactly one cell contains two ball and six ball randomly placed in 5 cells.

Therefore number of ways when exactly one cell is remains empty is ${}^6{C}_1\cdot {}^6{C}_2\cdot 5!$
Required probability $=\frac{{}^6{C}_1\cdot {}^6{C}_2\cdot 5!}{6^6}=\frac{25}{108}$