Answer to Question #314180 in Statistics and Probability for agbai

Question

12 students are to pose for photographs after a social gathering at FCT. 4 students are from Lagos state, 3 are from Kano state and the remaining are from Kwara state. How many possible photographs can they take if students from the same state must stand close to one another?

Answer 1

There are $3!=6$ ways to choose order of states from left to right. After the order of state is chosen we need to choose the order in each group of students from the same state, which is $4!\cdot 3!\cdot 5!=17280$ ways. Thus the total is $6\cdot 17280=103680$ ways.