There are 8 wild card and 25 of each 4 colored card which makes the total number of cards are: 8 + 25*4= 108 cards.
The number of ways to take 7 cards out of 108 cards would be:
108C7= 108! / (108-7)! 7!= 27883218168
1. Draw exactly 2 wild cards out of 7 cards
This condition can be interpreted as taking 2 wilds cards and 5 other cards
Number of ways to take 2 wilds cards out of 8 wild card = 8C2= 8!/6!2!= 28
After taking 2 cards, the stack would become 106 cards.
Number of ways to take 5 random cards out of remaining 106 random card= 106C5= 106!/(101!*5!)= 101340876
The probability would be:28 * 101340876/ 27883218168=0.1017= 10.17%
2. Draw exactly 2 wild, 2 red, 3 green out of 7 cards
You can solve this using the same principle.
2 wild card from 8 wild cards: 8C2 = 28
2 red card from 25 red cards: 25C2 = 25!/(23!*2!) = 300
3 green card from 25 green cards: 25C3 = 25!/(22!*3!)= 2300
The probability would be: 28*300*2300/ 27883218168= 0.00069= 0.07%