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Jack
07-20-2013, 03:27 PM
SAT math counting problems

I need help with the following question:

"In how many different ways can 4 students be seated in two seats?"

Thanks!!:D:D

Oliver
07-20-2013, 03:56 PM
SAT maths counting problem permutations

"In how many different ways can 4 students be seated in two seats?"

The number of ways you can change the order of a set of objects is called the number of PERMUTATIONS of that set of objects.

The total number of ways of arranging n objects, taking r at a time is gibe by the following formula:

{{P}^{n}}_{r}=\frac{n!}{(n-r)!}, where n!=1\cdot2\cdot3..\cdot n

So, in your case, you have 4 students taking 2 at a time

{{P}^{4}}_{2}=\frac{4!}{(4-2)!}=\frac{4!}{2!}=\frac{1\cdot 2\cdot 3\cdot 4}{1\cdot 2}=3\cdot 4=12 ways.

The above calculations could be done easily in your GDC casio fx-9860GII SD for example as follows:

OPTN>PROB>nPr and set n=4 and r=2

Another way to solve this problem is that the first seat can be filled with 4 ways and the second with the remaining 3ways(students). So, the total ways are 4x3=12

Hope these help!!:D

Jack
07-20-2013, 03:56 PM
Thanks Oliver!!