A counselor at a middle school must create an arranged schedule of elective classes for the last 2 periods of the day for all of the 6th grade students. The counselor has 12 electives courses (e. g. art, band, PE, etc.) to choose from and must select 2 ordered classes for each 6th grade student. How many ways can the counselor arrange the last 2 periods of the day for the 6th grade students?

Solution

The counselor has 12 electives courses (e.g. art, band, PE, etc.) to choose from and must select 2 ordered classes for each 6th grade student.

Let S be the sample space.

Then, n(S) = 12C2 = (12 x 11) ÷ (2 x 1 ) =  132 ÷ 2 =  66

Sixty six (66) ways can the counselor arrange the last 2 periods of the day for the 6th grade students

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w