Question

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.)

Answer 1

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.

Answer 2

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.

Answer 3

52*51=2625

Answer 4

i meant 2652