Help! -- Math Probability Question 2

Four cards are randomly selected from a standard 52-card deck. What is the probability of getting 4 hearts or 4 numbers less than 9 (count aces as 1)?

~Please show as much work as possible~

The probability of getting a heart on the first draw is 13/52. (There are 13 hearts remaining, and 52 total cards remaining.)
If you get a heart on the first draw, the odds of getting a heart on the second draw are 12/51. (You already pulled one heart, so 12 remain out of 51 remaining cards.)
If you have drawn two hearts, the odds of getting a heart on the third draw are 11/50.
If you have drawn three hearts, the odds of getting a heart on the fourth draw are 10/49.

So the probability of getting all 4 hearts are
13/52 * 12/51 * 11/50 * 10/49. That's 1,320 / 6,497,400, or 0.0002. (Or 0.02%. Now you know why flushes are so valuable in poker!)

Same principle applies for getting 4 numbers less than 9.
The odds of drawing one on the first draw are 32/52 (since there are 32 in the deck).
If you succeed, the odds of drawing one on the second draw are 31/51.
Then 30/50.
Then 29/49.

So the probability of drawing 4 cards all less than 9 are
32/52 * 31/51 * 30/50 * 29/49. That's 863,040 / 6,497,400, which is 0.1328, or 13.28%.

a. (13/52)^4 = 1/256
b. (32/52)^4 = 4096/28561
a x b = 16/28561

x/z = x over z.

13C4 * 4C1 / 52C4 = ?? ( 4 hearts)

8^4 / 52P4 = ?? ( 4 cards less than 9 )

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