Question

There are $9$ Indians, $5$ Americans and $2$ Japaneses in a hall. In how many ways they can be seated in a row such that persons of same nationality are to be seated together?

• A. $16!$
• B. $9!\times 5!\times 2!$
• C. $12\times 9!\times 5!$
• D. none of these

Answer 1

The correct option is C $12\times 9!\times 5!$

Take indians as 1 entity.

Americans as 1 entity.

japenese as 1 entity

So there are $3$ entities

While particular entities can be arranged among themselves.

Total number of ways $=9!\times 5!\times 2!\times 3!$