Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
898 views
in Permutations by (27.0k points)
closed by

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same color are indistinguishable?

1 Answer

+1 vote
by (24.8k points)
selected by
 
Best answer

Given, 

The disc : Red, Yellow, and Green. 

Total of 9 discs and it has 3 repeated discs Green, Red, and Yellow. 

The disc Green is repeated twice, and disc Red is repeated 4 times, disc Yellow is repeated thrice. 

To find : Number of the arrangement of discs. 

The problem can now be rephrased as to find total number of permutations of 9 objects (R, R, R, R, Y, Y, Y, G, G) of which three objects are of same type (Y, Y, Y), and two objects are of another type (G, G), and 4 objects are of different type (R, R, R, R). 

Since we know,

Permutation of n objects taking r at a time is nPr,and permutation of n objects taking all at a time is n! 

And, 

We also know,

Permutation of n objects taking all at a time having p objects of the same type, q objects of another type, r objects of another type is \(\frac{n!}{p!\times q!\times r!}\).

i.e., 

The number of repeated objects of same type are in denominator multiplication with factorial.

Total number of such permutations will be \(\frac{9!}{4!\times 2!\times 3!}\).

\(\frac{5\times 6\times 7\times 8\times 9}{(2\times 1)\times (3\times 2\times 1)}\)

= 1260 

Hence, 

Total number of permutations of the given type is 1260.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...