Question #194633

 Polya described four steps in the solving of a mathematics problem. Here is a problem: A classroom has 2 rows, each with 8 seats. Of 14 students, 5 always sit in the front row, and 4 always sit in the back row, and the rest sit in either row. In how many ways can the students be seated?

6.1.1 Use three different types of representations to model the problem

6.1.2 Now use the steps of Polya to solve this problem. You must explain in detailwhat you are doing in each step


1
Expert's answer
2021-05-18T17:38:18-0400

6.1.1

5 students can be seated in the first row in 8P5^8P_5 ways.


4 students can be seated in the second row in 8P4^8P_4 ways.


Remaining 5 students can be seated in remaining 7 seats in 7P5^7P_5 ways.


6.2.2

Total number of ways students can be seated is-


=8P5×8P4×7P5=8!3!×8!4!×7!2!=(8!)2×5.72=352(8!)2=^8P_5\times ^8P_4\times ^7P_5 \\[9pt] =\dfrac{8!}{3!}\times \dfrac{8!}{4!}\times \dfrac{7!}{2!} \\[9pt] =(8!)^2\times \dfrac{5.7}{2} \\[9pt] =\dfrac{35}{2}(8!)^2


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