Question

A panel for a political forum is made up of 14 people from three parties, all seated in a row. The panel consists of 1 Republican, 6 Green Party members, and 7 Democrats. In how many distinct orders can they be seated if two people of the same party are considered identical (not distinct)?

Answer 1

Given that

A panel for a political forum is made up of 14 people from three parties, all seated in a row.

The panel consists of 1 Republican, 6 Green Party members, and 7 Democrats.

For Republicans, they can be seated in 1 way.

For Green Party with 6 members, they can be arranged in

`2,2,2=3\text{ways}`

While in 7 Democrats, they can be arranged in

`2,2,2,1=4\text{ways}`

Therefore, if two people of the same party are considered identical, they can be arranged in

`1*3*4=12ways`

Hence, they can be arranged in 12 distinct orders.