If 7 identical white balls and 3 identical bl | 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 and $3$ black balls is $\frac{10!}{7!3!} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.To en

Vedclass · Accepted Answer

$7/15$

Vedclass · Answer

(B) Total number of ways to arrange $7$ white and $3$ black balls is $\frac{10!}{7!3!} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.To ensure no two black balls are together,we use the gap method. First,arrange the $7$ white balls: $\_ W \_ W \_ W \_ W \_ W \_ W \_ W \_$.There are $8$ possible gaps for the $3$ black balls.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 probability is $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{56}{120} = \frac{7}{15}$.

If $7$ identical white balls and $3$ identical black balls are arranged in a row at random,what is the probability that no two black balls are together?

Similar Questions

$A$ committee of $5$ is to be chosen from a group of $9$ people. The probability that a certain married couple will either serve together or not at all,is

If a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively is

Out of $13$ applicants for a job,there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is

$A$ container contains nine balls: three red,four blue,and two green. If three balls are selected at random from the container without replacement,what is the probability that all three balls are of different colors?

$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and $1$ spade?

Vedclass Test Series

Exam Paper Generator

Online Exam Module