Answer:
,
,
, ![\frac{9}{4802}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B4802%7D)
Step-by-step explanation:
The bag has a total of (4+2+3+5) = 14 balls. Set up the proportions:
Red: ![\frac{4}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B14%7D)
green: ![\frac{2}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B14%7D)
yellow: ![\frac{3}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B14%7D)
blue: ![\frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B14%7D)
Now solve!
Removing 1 yellow, 1 red, 1 green, and 1 blue = ![\frac{3}{14} \cdot \frac{4}{14} \cdot \frac{2}{14} \cdot \frac{5}{14} =\frac{15}{4802}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B14%7D%20%5Ccdot%20%5Cfrac%7B4%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B2%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B5%7D%7B14%7D%20%3D%5Cfrac%7B15%7D%7B4802%7D)
Removing 1 blue, 1 green, 1 green, and 1 yellow = ![\frac{5}{14} \cdot \frac{2}{14} \cdot \frac{2}{14} \cdot \frac{3}{14} =\frac{15}{9604}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B14%7D%20%5Ccdot%20%5Cfrac%7B2%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B2%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B3%7D%7B14%7D%20%3D%5Cfrac%7B15%7D%7B9604%7D)
Removing 1 red, 1 red, 1 yellow, and 1 yellow = ![\frac{4}{14} \cdot \frac{4}{14} \cdot \frac{3}{14} \cdot \frac{3}{14} =\frac{9}{2401}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B14%7D%20%5Ccdot%20%5Cfrac%7B4%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B3%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B3%7D%7B14%7D%20%3D%5Cfrac%7B9%7D%7B2401%7D)
Removing 1 green, 1 yellow, 1 yellow, and 1 red = ![\frac{2}{14} \cdot \frac{3}{14} \cdot \frac{3}{14} \cdot \frac{4}{14} =\frac{9}{4802}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B14%7D%20%5Ccdot%20%5Cfrac%7B3%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B3%7D%7B14%7D%20%20%5Ccdot%20%5Cfrac%7B4%7D%7B14%7D%20%3D%5Cfrac%7B9%7D%7B4802%7D)