Suppose that a group of 27 students are going to pose for a class photo.They are to be arranged in three rows with 10 in the front row, 6 in the middle row and 11 in the back row.The photographer selects which students go in each row.In how many different ways can the class now be arranged for the photo?

The total number of ways the students can be arranged is given by the number of ways to choose students for each row, multiplied by the number of ways to arrange the students within each row.

Step 1: Choose students for each row The number of ways to choose 10 students from 27 for the front row is given by the combination formula 27 choose 10, which is denoted as 27C10. Similarly, the number of ways to choose 6 students from the remaining 17 for the middle row is 17C6, and the remaining 11 students will go to the back row.

Step 2: Arrange students within each row The number of ways to arrange 10 students in the front row is given by the permutation formula 10!, similarly for the middle row it's 6!, and for the back row it's 11!.

So, the total number of ways to arrange the students is given by:

(27C10 * 10!) * (17C6 * 6!) * 11!

This simplifies to:

27! / (10! * 17!) * 10! * 17! / (6! * 11!) * 6! * 11!

The 10!, 6!, 17!, and 11! terms cancel out, leaving:

27! / (10! * 6! * 11!)

This is the final answer.