Q. 1.2 - A First Course in Probability

Question

If $4$ Americans, $3$ French people, and $3$ British people are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?

Step-by-Step Solution

Answer

The required no. of seating arrangements are $5184$.

Step 1. Given information.

It is given that,

No. of Americans = $4$

No. of French = $3$

No. of British = $3$

All these people are to be seated in a row. 

Step 2. Find the required no. of seating arrangements.

Three groups can be arranged in $=3! \text{ways}=3\times 2\times 1=6\text{ways}$

Four Americans can be arranged in = $4! \text{ways}=4\times 3\times 2\times 1=24\text{ways}$

Three French can be arranged in $=3! \text{ways}=3\times 2\times 1=6\text{ways}$

Three British can be arranged in $=3! \text{ways}=3\times 2\times 1=6\text{ways}$

Total no. of ways  $=6\times 24\times 6\times 6=5184$

Therefore, the required no. of seating arrangements are $5184$.