To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{6} \) ÷ \( \frac{1}{9} \) = \( \frac{2}{6} \) x \( \frac{9}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{6} \) x \( \frac{9}{1} \) = \( \frac{2 x 9}{6 x 1} \) = \( \frac{18}{6} \) = 3

To multiply terms with radicals, multiply the coefficients and radicands separately:

9\( \sqrt{2} \) x 5\( \sqrt{9} \)
(9 x 5)\( \sqrt{2 \times 9} \)
45\( \sqrt{18} \)

Now we need to simplify the radical:

45\( \sqrt{18} \)
45\( \sqrt{2 \times 9} \)
45\( \sqrt{2 \times 3^2} \)
(45)(3)\( \sqrt{2} \)
135\( \sqrt{2} \)

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:

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

You have 15 out of the total of 300 raffle tickets sold so you have a (\( \frac{15}{300} \)) x 100 = \( \frac{15 \times 100}{300} \) = \( \frac{1500}{300} \) = 5% chance to win the raffle.