### Instruction: How many ways are there to choose 3 cards from a standard deck of 52 cards, if all three cards must be of different suits?  (Assume that the order of the cards does not matter.).### Response: I need to count the number of combinations of 3 cards from different suits, without regard to order.
One way to approach this is to think of the suits as four bins, each containing 13 cards.
Then, to choose 3 cards from different suits, I need to pick one card from each of three bins, and leave one bin empty.
There are 4 ways to choose which bin to leave empty.
For each of these 4 choices, there are 13 ways to pick a card from the first bin, 13 ways to pick a card from the second bin, and 13 ways to pick a card from the third bin.
So, for each of these 4 choices, there are 13^3 ways to pick 3 cards from different suits.
Therefore, the total number of ways to choose 3 cards from different suits is 4 times 13^3.