Question 851815
This question is a combination question, because order does not matter.  The order of the students doesn't matter, and there can be no repetition.  So, the formula we will use to solve this, is:


{{{n!/(r!(n-r)!)}}}


n = the total number (17 in our problem)


r = the number taken (6 in our problem)


So, we will plug in 17 for n, and 6 for r in our formula:


{{{17!/(6!(17-6)!)}}}


This means:


{{{(17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/((6*5*4*3*2*1)(11*10*9*8*7*6*5*4*3*2*1))}}}


You can cross out any numbers that are in both the numerator and denominator.  Doing so will give you:


{{{(17*16*15*14*13*12)/(6*5*4*3*2*1)}}}


Now, just multiply the numbers in the numerator and the numbers in the denominator, and then divide.  So,


{{{8910720/720}}} ----->


{{{12376}}}.  So, there are 12,376 ways nature can select 6 students out of 17 to get the flu.