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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?

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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

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

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

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