Twelve balls are placed in three boxes. The probability that the first box contains three balls is

Question

Twelve balls are placed in three boxes. The probability that the first box contains three balls is

Twelve balls are placed in three boxes. The probability that the first box contains three balls is
A. `(110)/(9)((2)/(3))^(10)`
B. `(9)/(110)((2)/(3))^(10)`
C. `(.^12C_(3))/(12^(3))xx2^(9)`
D. `(.^(12)C_(3))/(3^(12))`

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

Related Questions

A box contains 12 balls out of which x are black. If 6 more black balls are put in the box, the probability of drawing a black ball

2 Answers 10 Views

A box contains 12 balls out of which x are black. If 6 more black balls are put in the box, the probability of drawing a black ball

2 Answers 5 Views

Three bags contain a number of red and white balls as follows Bag I : 3 red balls, Bag II : 2 red balls and 1 white balls and Bag III : 3 white balls.

2 Answers 10 Views

A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of dr

2 Answers 18 Views

Five different marbles are placed in 5 different boxes randomly. Then the probability that exactly two boxes remain empty is (each box can hold any nu

2 Answers 4 Views

A bag contains b blue balls and r red balls. If two balls are drawn at random, the probability drawing two red balls is five times the probability of

2 Answers 5 Views

An urn contains three red balls and n white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is `1//2

2 Answers 10 Views

A box `B_(1)` contains 1 white ball, 3 red balls, and 2 black balls. An- other box `B_(2)` contains 2 white balls, 3 red balls. A third box `B_(3)` co

2 Answers 6 Views

`5` different balls are placed in `5` different boxes randomly. Find the probability that exactly two boxes remain empty. Given each box can hold any

2 Answers 8 Views

A box contains `4` white and `3` black balls. Another box contains `3` white and `4` black balls. A die is thrown. If it exhibits a number greater tha

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A
Since each ball can be placed in any one of the 3 boxes, therefore there are 3 ways in which a ball can be palced in any one of the three boxes. Thus, there are `3^(12)` ways in which 12 balls can be placed in 3 boxes. The number of ways in which 3 balls out of 12 can be put in the box is `.^(12)C_(3)`. The remaining 9 balls can be placed in 2 boxes in `2^(9)` ways. So, required probability is
`(.^(12)C_(3))/(3^(12)) 2^(9) = (110)/(9) ((2)/(3))^(10)`