There are 4 seats available at a table in the lunch room of an elementary school, and 12 students are looking for seats. In how many ways can the seats at the table be filled with 4 of these 12 students?

Answer with explanation:Total number of vacant seats = 4 seatNumber of students Looking for Seats = 12 StudentWe have to fill the four Seats and there are 12 students.First Seat can be filled in 12 ways,11 students are left,So, second seat can be filled in 11 ways ,Now,there are 10 students left ,So, third seat can be filled in 10 ways,Now there are 9 students left,so last seat can be filled in 9 ways.Total number of ways of filling 4 seats if there are 12 number of students                =12 × 11 × 10 × 9               =132 × 90              =  11880 waysOr ,you can solve it directly by the concept of Permutation.Total ways of filling 4 vacant seats if there are 12 students in all            [tex]= _{4}^{12}\textrm{P}=\frac{12!}{(12-4)!}=\frac{12\times 11\times 10\times 9\times 8!}{8!}=12\times 11\times 10\times 9=11880[/tex]