suppose we have two rows and each contain 5 seats and we have 5 girls(girl 1,2,3,4,5) and 5 boys(boy 1,2,3,4,5) What are the number of cases that all boys sat together or girl 1 and 2 sat next to each other?
This is what I have done: $5!\cdot5!\cdot2+8\cdot8!\cdot2=\text{answer}$ But I am 100% sure I did over counting, my question in how to fix those over counting.