Question

if a coin is tossed 6 times, and then a standard six-sided die is rolled 2 times, and finally a group of three cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

Explanation:

Calculate coin toss outcomes

Using the Fundamental Counting Principle knowledge point

$$ N_{\text{coin}} = 2^6 = 64 $$

Calculate die roll outcomes

Using the Fundamental Counting Principle knowledge point

$$ N_{\text{die}} = 6^2 = 36 $$

Calculate card drawing outcomes

Using the Combinations knowledge point

$$ N_{\text{cards}} = \binom{52}{3} = \frac{52 \times 51 \times 50}{3 \times 2 \times 1} = 22,100 $$

Calculate total combined outcomes

Using the Fundamental Counting Principle knowledge point

$$ N_{\text{total}} = N_{\text{coin}} \times N_{\text{die}} \times N_{\text{cards}} = 64 \times 36 \times 22,100 = 50,918,400 $$

Answer:

\(50,918,400\)