The deck of a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand. What is the probability that a hand will contain exactly two wild cards? What is the setup for this problem (that you would type into your calculator)? (Do not actually find the probability.)

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 = ?

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.