Aspire Faculty ID #11493 · Topic: CUET 2022 · Just now
CUET 2022

4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Answer the following questions.

The number of ways of arranging them so that the three Americans should sit together is:

Solution

Short Solution:

Total people = 4 Indians + 3 Americans + 2 Britishers = 9
Since arrangement is around a circular table, we fix one position ⇒ remaining to arrange: 8 positions

Group the 3 Americans together as a single unit ⇒ total units = 4 Indians + 1 American group + 2 Britishers = 7 units
Circular arrangement of 7 units = \( (7 - 1)! = 6! \)

Internal arrangements of 3 Americans = \( 3! \)

Total arrangements =
$$6! \times 3! = 720 \times 6 = \boxed{4320}$$
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Yusra
Yusra , Aspirant
Commented Mar 18, 2024
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