10 students line up for a picture They can either all line u

10 students line up for a picture. They can either all line up in one row of ten, or they can line up in two rows of five. How many unique ways can they line up for the photograph?

Solution

Lining up for a row of 10, there are 10! ways.

Lining up in two rows of 5, there are 10P5 ways for the first row, and 5P5 ways for the second row.

Thus, there are 10! + 10P5 + 5P5 = 3659160 ways. [ANSWER]