Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • In how many ways can the red balls be arranged if there are 11 identical red balls, 9 identical blue balls, and 7 identical green balls such that at least one green ball

In how many ways can the red balls be arranged if there are 11 identical red balls, 9 identical blue balls, and 7 identical green balls such that at least one green ball separates any two red balls?

 

Option: 1

792


Option: 2

102


Option: 3

850


Option: 4

356


Answers (1)

best_answer

To calculate the number of ways the red balls can be arranged under the given conditions, where at least one green ball separates any two red balls, we can use the concept of permutations.

We have 11 identical red balls, 9 identical blue balls, and 7 identical green balls. We need to ensure that at least one green ball is placed between any two red balls.

We can treat the green balls as dividers or separators between the red balls. Let's represent the arrangement using "R" for red balls and "|" for green ball separators:

R | R | R | R | R | R | R | R | R | R | R |

Now, we need to place the 7 green balls in the spaces between the red balls and at the ends of the arrangement. We have 12 spaces (represented by the "|" symbols) where we can place the green balls.

Using the concept of stars and bars, we need to select 7 out of the 12 spaces to place the green balls. We can calculate this using the combination formula \mathrm{(n C r):}

\mathrm{\begin{aligned} & C(12,7)=12 ! /(7 ! \times(12-7) !) \\ & =12 ! /(7 ! \times 5 !) \\ & =(12 \times 11 \times 10 \times 9 \times 8) /(5 \times 4 \times 3 \times 2 \times 1) \\ & =792 \end{aligned}}

 

Posted by

mansi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE 2026: IIT admissions show major shift toward AI, data science, away from core engineering courses
anam-khan

JEE Main 2026: NIT Delhi cut-offs for BTech courses show ever-increasing demands for AI, computer skills
anam-khan

597 Eklavya school students clear JEE, NEET exams in 2024-25; Gujarat, MP lead

Latest Question