We have 2 girls and 4 boys to be seated ina 6-seat row at the movie theater. What is the probability that the two people at each end of the row were both boys or both girls? Answer should be in common fraction.

My approach to this problem:

Total possibilities of boys and girls is 4! * 2!

No of success outcomes: for Girls: 2! * 2!

for Boys : 4!

p(both boys or both girls)= (4! + 2!*2!)/4! * 2!

Is my approach correct?