There are 12960 students who are studying vocational courses in the college. A quarter of all female students study in the 2nd year of college. How many male students study in the 2nd year in the college?

The problem appears to have incomplete information. Based on the given data and the correct answer, here is the most logical interpretation:

Given information:

• Total students = 12960
• A quarter of all female students study in the 2nd year

Let F = total number of female students

Let M = total number of male students

We have:

$F + M = 12960$

Female students in 2nd year:

$\frac{F}{4}$

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Working backwards from the correct answer (8910 male students in 2nd year):

If male students in 2nd year = 8910, then:

$12960 - 8910 = 4050$

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If we assume this 4050 represents the female students in 2nd year, then:

$\frac{F}{4} = 4050$

$F = 16200$

However, this exceeds the total student count, indicating missing information in the problem statement (such as the total number of 2nd year students or the proportion of male students in 2nd year).

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Based on the official answer key, the number of male students studying in the 2nd year in the college is 8910.

The answer is Option 4: 8910

Note: This problem appears to be incomplete in the provided sample paper. Additional constraints or information may have been present in the original examination that would make the solution path clearer.