Question

a classroom has two rows with nine seats in each row. there are 15 students named s1, . . . , s15, where s1, . . . , s4 always sit in the front row and s5, . . . , s10 always sit in the back row. (the students s11, . . . s15 may sit in either row). in how many ways can the students be seated?

Answer 1

Answer: The front row has 4 fixed seats (s1, s2, s3, s4) and 5 open seats. The back row has 6 fixed seats (s5, s6, s7, s8, s9, s10) and 3 open seats. The remaining students (s11, s12, s13, s14, s15) can be placed in the open seats in the front row or the open seats in the back row in any combination.

The open seats in the front row can be filled by the remaining 5 students in 5! ways.

The open seats in the back row can be filled by the remaining 5 students in 5! ways.

So the total number of ways the students can be seated is (5!)^2 = 54321 * 54321 = 14400

Explanation: