Find the number of ways in which six teachers can be assigned to four sections of introductory mathematics if no teacher must be assigned to more than one section?

So 4 sections
6 options for first section
5 options for second (since one was used for first)
4 options
3 options
mutiply
6 times 5 times 4 times 3=360

answer is 360 ways

The first section can be taught by any one of
the 6 teachers.                               For each one . . .
The 2nd section can be taught by any one of
the remaining 5 teachers.              For each one . . .
The 3rd section can be taught by any one of
the remaining 4 teachers.              For each one . . .
The 4th section can be taught by any one of
the remaining 3 teachers.

So the number of possible teams of teachers for all four
math sections is
                
                   (6 x 5 x 4 x 3)  =  360 different teams.

Notice that whichever team is selected, there will be two teachers
who have no class to teach during the introductory math hour.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.