the question asks:
How many 5-card poker hands consisting of 2aces and 3 kings are possible with an ordinary 52-card deck?
this is what i did:
"c"=stands for combination
(4C2) * (4C3) = 6*4 = 24
(52C5) = 259860
so then i divided :
(24)/(259860)= 9.2344630159756210176378243605134e-6
Looks right.
Cept the question asks for the number of possible hands; I would have stopped at 24. But, good job, you went further and gave the probability of drawing such a hand.
You have correctly calculated that there are 24 possible 5-card poker hands consisting of 2 aces and 3 kings in an ordinary 52-card deck.
To arrive at this answer, you used the combination formula "C" to calculate the number of ways to choose 2 aces from the 4 available aces (4C2), and multiplied it by the number of ways to choose 3 kings from the 4 available kings (4C3).
Then, you divided this number (24) by the total number of possible 5-card poker hands that can be formed from a standard 52-card deck (52C5), which is equal to 259,860.
As a result, you obtained the probability of randomly drawing a 5-card poker hand with 2 aces and 3 kings, which is approximately 9.23 × 10^(-6), or 0.00000923.
Great job on your calculations!