Question

In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated in a row so that those of the same nationality sit together?

Answer 1

Answer (13 of the original arrangements are duplicates now, as AAAF F F FDDDDCC, AAF F F FDDDDCCA, ..., CAAAF F F FDDDDC are identical): 900900/13 = 69300.

Answer 2

Answer:

165888

Step-by-step explanation:

Given,

Number of americans = 3,

Total way of seating americans in 3 seats = 3 !,

Number of frenchmen = 4,

Total way of seating frenchmen in 4 seats = 4 !,

Number of danes = 4

Total ways of seating danes in 4 seat = 4 !,

Also, number of Italians = 2,

Total ways of seating italians in 2 seats = 2 !,

Hence, the total ways of seating all citizens so that people with same nationality sit together  =  ( 3! × 4! × 4! × 2! ) × 4!

= 6 × 24 × 24 × 2 × 24

= 165888