The total number of balloons is 40 (10 pink + 9 yellow + 12 green + 9 white).

We need to find the probability of selecting exactly 3 green balloons out of 7 selected balloons.

Using combinations, the number of ways to choose 3 green balloons from 12 is given by:

\(\binom{12}{3}\)

The number of ways to choose the remaining 4 balloons from the 28 non-green balloons is:

\(\binom{28}{4}\)

The total number of ways to choose 7 balloons from 40 is:

\(\binom{40}{7}\)

The probability is then given by:

\(\frac{\binom{12}{3} \times \binom{28}{4}}{\binom{40}{7}}\)

Calculating each part:

\(\binom{12}{3} = 220\)

\(\binom{28}{4} = 20475\)

\(\binom{40}{7} = 18643560\)

Thus, the probability is:

\(\frac{220 \times 20475}{18643560} = 0.242\)