Certainly! Let's solve this step-by-step.
1. Understanding the deck: A standard deck of cards has 52 cards, composed of 4 suits (hearts, diamonds, clubs, spades), each with 13 ranks (from Ace to King).
2. Picking an Ace:
- There are 4 Aces in a standard deck (Ace of hearts, Ace of diamonds, Ace of clubs, Ace of spades).
- Since we are picking one Ace, there are 4 possible ways to do this.
3. Picking a Heart:
- There are 13 hearts in the deck (one for each rank from Ace to King).
- Since we put the Ace back, the total number of cards is still 52.
- So, there are 13 possible ways to choose a heart.
4. Picking a Five:
- There are 4 fives in a standard deck (five of hearts, five of diamonds, five of clubs, five of spades).
- Since we put the heart back, there are still 52 cards in the deck.
- Therefore, there are 4 possible ways to choose a five.
5. Calculating the total number of ways:
- Since each event (picking an Ace, picking a heart, picking a five) is independent, we multiply the number of ways these events can occur.
[tex]\[
\text{Total number of ways} = (\text{Number of ways to pick an Ace}) \times (\text{Number of ways to pick a Heart}) \times (\text{Number of ways to pick a Five})
\][/tex]
Substituting the values:
[tex]\[
\text{Total number of ways} = 4 \times 13 \times 4
\][/tex]
Calculating this product:
[tex]\[
4 \times 13 = 52
\][/tex]
[tex]\[
52 \times 4 = 208
\][/tex]
So, there are 208 ways to pick an Ace, a heart, and a five from a standard deck, assuming you put the cards back into the deck after each pick.
