How many combinations of 4 students can a teacher choose from 30 students?

a. 27,405

b. 657,720

c. 120

d.810,000

b.  27,405

Step-by-step explanation:

So, we have a total population of 30 (n) and we sample 4 (r) from it.

Now, is it a combination or a permutation?  Does the order matter?  Is it important that the teacher picked John before Andrew?  No.  So, it's a combination:

C(n,r)=C(30,4)

So, the teacher has 27,405 ways to combine groups of 4 students from his 30-student class.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1