A standard deck of 52-card deck is used to play a game. Four cards are drawn. What is the probability that all four cards are diamonds?

I got this question wrong. I do not know how to solve it. Please explain.

Thanks

to start out, there are 13 diamonds in 52 cards. As you draw the cards, the probabilities change, due to the makeup of the remaining cards. The result is

13/52 * 12/51 * 11/50 * 10/49
= (13*12*11*10)/(52*51*50*49)
= 13P4/52P4

To solve this question, we need to calculate the probability of drawing four diamonds from a standard deck of 52 cards.

Step 1: Determine how many total outcomes are possible.
In a standard deck, there are a total of 52 cards.

Step 2: Determine how many favorable outcomes are possible.
Since we want to draw four diamonds, there are 13 diamonds in a deck. So, the first card we draw can be any of the 13 diamonds, the second card can be any of the remaining 12 diamonds, the third card can be any of the remaining 11 diamonds, and the fourth card can be any of the remaining 10 diamonds.

Step 3: Calculate the probability.
The probability is obtained by dividing the number of favorable outcomes by the number of total outcomes.
Number of favorable outcomes = 13 * 12 * 11 * 10 (since each card draw is independent)
Number of total outcomes = 52 * 51 * 50 * 49 (since each card draw is independent and we have a total of 52 cards in the deck)

Probability = (13 * 12 * 11 * 10) / (52 * 51 * 50 * 49)

Simplifying this expression gives us the probability that all four cards drawn are diamonds.