Question

Six balls are placed randomly into six cells.
Then the probability that exactly one cell
remains empty is
(A)29/216
(B)35/216
(C)25/108
(D)31/108​

Answer 1

0 either question is wrong or Ur option (•‿•)

Answer 2

Step-by-step explanation:

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

• Six balls are put randomly into six cells. Therefore total number of balls or outcomes will be 6^6  
• So we need to find the probability of the ways that exactly one cell remains empty  
• So we have
• Required ways will be
• In 6 cells one cell will be empty so it will be 6 C1
• Now in 6 cells if 5 balls are kept and we need to select one cell from 5 cells. So it will be 5C4
• 6 C1 x 5 C 4 x 6! / 2!
• 6 C1 = 6! / 1! (6 – 1)!
•         = 6! / 5!
•         =6
• 5C4 = 5! / 4! (5 – 4)!
•         = 5! / 4!
•        = 5
• 6! / 2! = 6 x 5 x 4 x 3 x 2 x 1 / 2 x 1
•           = 3600
• So we get 6 x 5 x 3600 = 10,800
• Therefore probability = number of possible outcomes / total number of outcomes
•                                       = 10,800 / 6^6
•                                       = 10,800 / 46656
•                                       = 25 / 108

Reference link will be

https://brainly.in/question/7569612