Ex: Find the probability of drawing 3 aces at random from a deck of 52 ordinary cards if the cards are not replaced.
Here's what I did:
The probability of choosing the first ace = $\dfrac{^4C_1}{^{52}C_1}$
The probability of choosing the second ace = $\dfrac{^3C_1}{^{51}C_1}$
The probability of choosing the third ace = $\dfrac{^2C_1}{^{50}C_1}$
The probability is = $\dfrac{^4C_1}{^{52}C_1}\times\dfrac{^3C_1}{^{51}C_1}\times\dfrac{^2C_1}{^{50}C_1}=\dfrac{1}{5525}$
But the answer is given as $\dfrac{1}{17,576}$
Please tell me where did I go wrong?
Best Answer
As a number of prople have already pointed out, your answer is correct.
However, if you are using combinations, it would be good to write it as ${4\choose 3}$/${52\choose 3}$
You could also directly work it out as $\frac {4\cdot 3\cdot 2} {52\cdot 51\cdot 50}$