The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 have in common.

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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:

\( \sqrt{\frac{64}{49}} \)
\( \frac{\sqrt{64}}{\sqrt{49}} \)
\( \frac{\sqrt{8^2}}{\sqrt{7^2}} \)
\( \frac{8}{7} \)
1\(\frac{1}{7}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 7}{3 x 7} \) - \( \frac{6 x 3}{7 x 3} \)

\( \frac{21}{21} \) - \( \frac{18}{21} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{21 - 18}{21} \) = \( \frac{3}{21} \) = \(\frac{1}{7}\)

You have 28 out of the total of 350 raffle tickets sold so you have a (\( \frac{28}{350} \)) x 100 = \( \frac{28 \times 100}{350} \) = \( \frac{2800}{350} \) = 8% chance to win the raffle.