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?

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

11520

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To calculate the total number of different curricula available for the student's consideration, we need to multiply the number of options for each course.

The student can select one of four business courses, so we start with 4 options. Then, the student can choose one of four mathematics courses, giving us 4 options again.

For the elective courses, the student needs to choose two out of ten options. We can calculate this using combinations. Since the order of the two elective courses doesn't matter, we use the formula for combinations, denoted as "nCr", where "n" is the total number of options and "r" is the number of selections. So, the number of combinations for selecting two out of ten is calculated as:

10C2 = (10!)/[(2!) * (10-2)!] = (10 * 9)/[(2 * 1)] = 45

Next, the student must choose either one of four history courses or one of four social science courses. This represents an "either-or" situation, so we add these two options together, giving us 4 + 4 = 8 options.

Finally, we multiply all of the options together to get the total number of curricula available:

Total options = (4 business courses) * (4 mathematics courses) * (45 elective combinations) * (8 history/social science courses)

Total options = 4 * 4 * 45 * 8 = 5,760

Therefore, there are 5,760 different curricula available for the student's consideration when selecting one business course, one mathematics course, two elective courses, and either one history or one social science course.