If a coin is tossed 3
 times, and then a standard six-sided die is rolled 3
 times, and finally a group of five cards are drawn from a standard deck of 52
 cards without replacement, how many different outcomes are possible?

To find how many different outcomes are possible, let's break the problem into its three distinct parts:

### 1. Coin Tossed 3 Times:
Each coin toss has 2 possible outcomes (Heads or Tails), and since the coin is tossed 3 times, the number of possible outcomes is:

\[
2^3 = 8
\]

### 2. Die Rolled 3 Times:
Each roll of a standard six-sided die has 6 possible outcomes. Since the die is rolled 3 times, the number of possible outcomes is:

\[
6^3 = 216
\]

### 3. Five Cards Drawn Without Replacement:
From a standard deck of 52 cards, we are selecting 5 cards without replacement. The number of ways to choose 5 cards from 52 can be found using the combination formula:

\[
\binom{52}{5} = \frac{52!}{5!(52-5)!} = \frac{52 \times 51 \times 50 \times 49 \times 48}{5 \times 4 \times 3 \times 2 \times 1} = 2,598,960
\]

### Total Number of Different Outcomes:
The total number of different outcomes is the product of the outcomes from each stage:

\[
\text{Total outcomes} = 2^3 \times 6^3 \times \binom{52}{5}
\]

\[
\text{Total outcomes} = 8 \times 216 \times 2,598,960
\]

\[
\text{Total outcomes} = 4,494,110,080
\]

So, the total number of different outcomes is **4,494,110,080**.

Would you like a more detailed explanation on any part?

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### 5 Related Questions:
1. How many outcomes are possible if the coin is tossed 4 times instead of 3?
2. What is the probability of drawing 5 cards of the same suit from a deck?
3. How would the total outcomes change if the die is rolled 4 times?
4. What if we draw 4 cards instead of 5 from the deck of 52? How many outcomes are possible?
5. Can the combination formula be applied if the cards were drawn **with** replacement?

### Tip:
When calculating combinations (like card draws), remember that **order doesn't matter**. For outcomes where order matters, you'd use **permutations** instead.

If a coin is tossed 3 times, and then a standard six-sided die is rolled 3 times, and finally a group of five cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

Discover how to calculate the total number of outcomes when a coin is tossed 3 times, a die is rolled 3 times, and 5 cards are drawn from a standard deck without replacement. Learn about the application of probability and combinatorics in this detailed step-by-step solution, suitable for Grades 10-12.

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