A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{35}{100} \) = \( \frac{35 x 20}{100} \) = \( \frac{700}{100} \) = 7 shots

The center makes 25% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{7}{\frac{25}{100}} \) = 7 x \( \frac{100}{25} \) = \( \frac{7 x 100}{25} \) = \( \frac{700}{25} \) = 28 shots

to make the same number of shots as the guard and thus score the same number of points.

The number of students taking German or Spanish is 10 + 15 = 25. Of that group of 25, 8 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 25 - 8 = 17 who are taking at least one language. 27 - 17 = 10 students who are not taking either language.

The factors of 76 are [1, 2, 4, 19, 38, 76] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 the greatest factor 76 and 68 have in common.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{9 + 5 + 8 + 6}{4} \) = \( \frac{28}{4} \) = 7