A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\heartsuit$ and $\diamondsuit$, called 'hearts' and 'diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called 'spades' and 'clubs') are black. The cards in the deck are placed in random order (usually by a process called 'shuffling'). In how many ways can we pick two different cards? (Order matters, thus ace of spades followed by jack of diamonds is different than jack of diamonds followed by ace of spades.)

For the total number of possibilities, there are 52 ways to pick the first card, then 51 ways to pick the second card, for a total of $52 \times 51 =

2652 total possibilities.

since all the cards are different, this is just

52P2 = 52*51 = 2652

Think about it. There are 52 choices for the first card.
For each of those choices there are 51 ways to pick the next card.

52*51=2625

i meant 2652

Well, let's calculate it together, shall we?

To pick the first card, we have 52 choices because there are 52 cards in total.

Now, for the second card, since we want it to be different from the first card, we must choose from the remaining 51 cards.

So, the total number of ways to pick two different cards would be 52 multiplied by 51, which is 2,652.

However, since order matters (as stated in the question), we must also consider that the order of picking the cards can be different.

So, for each choice of the first card, we have 51 choices for the second card, resulting in a total of 52 multiplied by 51 multiplied by 2, which is 5,304.

Therefore, there are 5,304 different ways to pick two cards from a standard deck. That's quite a lot of possibilities!

To solve this problem, we can break it down into two steps:

Step 1: Choose the first card
Since there are 52 cards in the deck, we can choose the first card in 52 ways.

Step 2: Choose the second card
After choosing the first card, there are 51 cards left in the deck. We can choose the second card in 51 ways.

Since the order of the cards matters, the total number of ways to pick two different cards is given by the product of the number of ways for each step:

Total number of ways = number of ways for step 1 * number of ways for step 2
= 52 * 51

Therefore, there are 52 * 51 = 2,652 ways to pick two different cards from a standard deck.