You have 7 out of the total of 250 raffle tickets sold so you have a (\( \frac{7}{250} \)) x 100 = \( \frac{7 \times 100}{250} \) = \( \frac{700}{250} \) = 3% chance to win the raffle.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{64}} \)
\( \frac{\sqrt{4}}{\sqrt{64}} \)
\( \frac{\sqrt{2^2}}{\sqrt{8^2}} \)
\(\frac{1}{4}\)

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:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

48,000 fans x \( \frac{2}{3} \) = \( \frac{96000}{3} \) = 32,000 fans.

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{52} \) = \( \frac{\frac{32}{4}}{\frac{52}{4}} \) = \( \frac{8}{13} \)