Four objects in a set of ten objects are alike. Find the number of ways of arranging them in a circular order. - Mathematics and Statistics

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Sum

Four objects in a set of ten objects are alike. Find the number of ways of arranging them in a circular order.

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Solution

There are 10 objects.
These 10 objects can be arranged in a circular order in (10 – 1)! = 9! ways.
∴ n = 9!
Out of 10 objects, 4 are alike.
r = 4
∴ Required number of arrangements

= `("n"!)/("r"!)`

= `(9!)/(4!)`

Concept: Permutations - Circular Permutations
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Chapter 6: Permutations and Combinations - Exercise 6.5 [Page 85]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.5 | Q 9 | Page 85

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