From a deck of 52 cards, how many different four-card hands could be dealt which include one card from each suit?

ok thanks I just wanted to make sure I did it right

To determine the total number of different four-card hands that include one card from each suit, we can break down the problem into four steps, one for each suit:

Step 1: Select one card from the first suit (Spades)
There are 13 cards in each suit, so there are 13 ways to select one card from the Spades suit.

Step 2: Select one card from the second suit (Hearts)
After selecting one card from the Spades suit, there are only 12 cards left in each suit. So, there are 12 ways to select one card from the Hearts suit.

Step 3: Select one card from the third suit (Diamonds)
After selecting one card from the Spades and Hearts suits, there are only 11 cards left in each suit. So, there are 11 ways to select one card from the Diamonds suit.

Step 4: Select one card from the fourth suit (Clubs)
After selecting one card from the Spades, Hearts, and Diamonds suits, there are only 10 cards left in each suit. So, there are 10 ways to select one card from the Clubs suit.

To find the total number of different four-card hands, we need to multiply the number of ways at each step:

Total number of different four-card hands = Number of ways in Step 1 * Number of ways in Step 2 * Number of ways in Step 3 * Number of ways in Step 4
= 13 * 12 * 11 * 10
= 15,120

Therefore, there are 15,120 different four-card hands that could be dealt, each including one card from each suit.

To find the number of different four-card hands that could be dealt, which include one card from each suit, we need to consider the following:

1. Number of suits: A standard deck of cards has four suits - hearts, diamonds, clubs, and spades. So, we have four choices for the card from the first suit, three choices for the card from the second suit, two choices for the card from the third suit, and one choice for the card from the fourth suit.

2. Number of cards per suit: In each suit, there are 13 cards (Ace, 2-10, Jack, Queen, and King).

To calculate the total number of different four-card hands, we multiply the number of choices for each suit:

4 * 3 * 2 * 1 = 24

Therefore, there are 24 different four-card hands that could be dealt, each including one card from each suit.

We need one form the hearts, one from the clubs etc.

number = C(13,1)x C(13,1) x C(13,1) x C(13,1)
= 13^4 = ....