A student planning her curriculum for the upcoming year must select one of four business courses, one of four mathematics courses, two of ten elective courses, and either one of four history courses or one of four social science courses. How many different curricula are available for her consideration?

Question

MathMate · Answer

Mike, Nicole and Kim, do please use the same pseudonym in your posts, because it helps to improve continuity.

We do not do repetitive exercises, that's your duty and privilege.

However, if each question brings up a new facet of the subject, we're glad to help/explain each.

For this problem, make a bijection onto the number of digits of the licence plate. That means that there is a one-to-one correspondence each way, so the count of one problem is the same as the count of the other.

B: 4
M: 4
E: 2 out of 10
H: 4 or S: 4 ≡ 4+4=8

Since she is not allowed to take two of the same Elective courses, there are only (10-1)=9 choices for the second.

So the total number of courses is
4²*10*9*8

Joe · Answer

11520

Answer

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