Seven white balls and three black balls are r | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Total number of ways to arrange $7$ white balls and $3$ black balls in a row is $\frac{10!}{7!3!} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes

Vedclass · Accepted Answer

$\frac{7}{15}$

Vedclass · Answer

(B) Total number of ways to arrange $7$ white balls and $3$ black balls in a row is $\frac{10!}{7!3!} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$. To ensure no two black balls are adjacent,we place the $7$ white balls first,creating $8$ possible gaps (including ends) where the $3$ black balls can be placed. The number of ways to choose $3$ gaps out of $8$ is $\binom{8}{3} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$. The required probability is $\frac{\binom{8}{3}}{\binom{10}{3}} = \frac{56}{120} = \frac{7}{15}$.

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

Similar Questions

What is the mixture of $MgCl_2$ and $MgO$ called?

Let electronegativity,ionisation energy and electron affinity be represented as $EN$,$IP$ and $EA$ respectively. Which one of the following equations is correct according to Mulliken?

$A$ radioactive sample $S_1$ having an activity of $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ can be

Which enzyme stimulates the germination of barley seeds?

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$. If the difference between the two lengths is independent of temperature,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module