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# probability question

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The deck for a card game contains 30 cards. 10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards. Each player is randomly dealt a five-card hand.

a) What is the probability that a hand will contain exactly two wild cards?

b) What is the probability that a hand will contain two wild cards, two red cards, and one blue cards?

Aug 12, 2020

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The deck for a card game contains 30 cards. 10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards. Each player is randomly dealt a five-card hand.

a) What is the probability that a hand will contain exactly two wild cards?

$$\text{Prob of exactly 2 wild cards}\\ =\frac{\text{number with exactly 2 wild cards}}{\text{number of possible hands}}\\ =\frac{4C2 * 26C3}{30C5}\\ =\frac{4!26!}{2!2!3!23!}\times \frac{5!25!}{30!}\\ =\frac{24*25*26}{1}\times \frac{2*3*4*5}{26*27*28*29*30}\\ =\frac{6*5}{1}\times \frac{2*3*4*5}{27*7*29*6}\\ =\frac{5}{1}\times \frac{2*4*5}{9*7*29}\\ = \frac{200}{1827}\\$$

I have not checked my working.

Aug 12, 2020