Math problem?

Question 012


Solve the problem.


Professor Kafka teaches an advanced probability class with an enrollment of 14 students. The front row has 9 chairs. A particular student, Carl, must sit in the front row between his tutor, Sue, and his best friend, Pat. In how many different ways can Professor Kafka assign students to sit in the first row?





a. 332640 b. 665280 c. 2328480 d. 4656960

Math problem?
Carl must sit between two people in the front row, so he must sit in the 2, 3, 4, ..., or 8th chair (7 possibilities)





So, 7*2*11*10*9*8*7*6 = 4656960





2, because either Sue on the left, or Pat on the left.





11*10*9*8*7*6, because apart from the three people, 6 others out of 11 can be seated in the front.
Reply:2 for the switch with Sue and Pat


7 for the number of chairs Carl can sit in


11! for the combination of the other students


5! for the chairs in the back row divided out (their order doesn't count)





2 * 7 * 11!/5! = 4656960 D is the correct answer