Given Information:
Total cards = 108
Red cards = 25
yellow cards = 25
Blue cards = 25
Green cards = 25
Wild cards = 8
Required Information:
Probability that a hand will contain exactly two wild cards in a seven-hand game = ?
Answer:
P = (₈C₂*₁₀₀C₅)/₁₀₈C₇
Step-by-step explanation:
The required probability is given by
P = number of ways of interest/total number of ways
The total number of ways of dealing a seven-card hand is
₁₀₈C₇
We want to select exactly 2 wild cards and the total wild cards are 8 so the number of ways of this selection is
₈C₂
Since the game is seven-card hand, we have to get the number of ways to select remaining 5 cards out of (108 - 8 = 100) cards.
₁₀₀C₅
Therefore, the setup for this problem becomes
P = number of ways of interest/total number of ways
P = (₈C₂*₁₀₀C₅)/₁₀₈C₇
This is the required setup that we can type into our calculators to get the probability of exactly two wild cards in a seven-hand card game with 8 wild cards and 108 total cards.