Forty discrete math students are to be divided into eight discussion groups, each consisting of five students. In how many ways can this be done?

Step-by-step explanation:

Given data

the number of students n=40

the number of groups r= 8

We are going to use the combination approach to solve the problem

nCr= n!/r!(n-r)!

substituting into the expression for the number of ways we have

40C8= 40!/8!(40-8)!

nCr= 40!/8!(32)!

nCr= 40!/8!(32)!

nCr= 40*39*38*37*36*35*34*33*32!/8!(32)!

nCr= 40*39*38*37*36*35*34*33*/8!

nCr= 40*39*38*37*36*35*34*33*/8*7*6*5*4*3*2

nCr= 3100796899200/40320

nCr=76904685 ways

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c