Find the number of ways of arranging 6 red ba | vedclass

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

Question

(D) First,arrange the $6$ red balls in a row. The number of ways to arrange $6$ identical red balls is $1$ (since they are identical),but if we treat

Vedclass · Accepted Answer

$7 	imes 6! 	imes 6!$

Vedclass · Answer

(D) First,arrange the $6$ red balls in a row. The number of ways to arrange $6$ identical red balls is $1$ (since they are identical),but if we treat them as distinct for the sake of permutation logic,it is $6!$. However,usually,balls of the same color are considered identical. Assuming the balls are distinct,the arrangement is $6!$. There are $7$ possible gaps created by $6$ red balls (including the ends) to place the $6$ black balls: $\_ R \_ R \_ R \_ R \_ R \_ R \_$. The number of ways to choose $6$ positions out of $7$ is $\binom{7}{6} = 7$. The number of ways to arrange $6$ black balls in these chosen positions is $6!$. Thus,the total number of arrangements is $6! 	imes \binom{7}{6} 	imes 6! = 6! 	imes 7 	imes 6! = 7 	imes 6! 	imes 6!$.

Find the number of ways of arranging $6$ red balls and $6$ black balls in a row such that no two black balls are together.

Similar Questions

In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?

Using the letters of the word $TRICK$,a five-letter word with distinct letters is formed such that $C$ is in the middle. In how many ways is this possible?

There are $9$ chairs in a room on which $6$ persons are to be seated. Out of these,one person is a guest who must occupy one specific chair. In how many ways can they sit?

In how many ways can the letters of the word $GARDEN$ be arranged such that the vowels appear in alphabetical order?

If the best and the worst paper never appear together,then in how many ways can $6$ examination papers be arranged?

Vedclass Test Series

Exam Paper Generator

Online Exam Module