Need help!

What is the probability of four cards of same value from a deck of cards???

#Combinatorics

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

I assume it's a deck of poker cards with 52 distinct cards and no jokers. Well, obviously you need to have the first card drawn, which can be anything.

Then the second, third, fourth card must be of the same value with the first card.

The probability that the second card is the same as the first card is equivalent of choosing 1 out 3 remaining cards out of 51 cards.

The probability that the second card is the same as the first card is equivalent of choosing 1 out 2 remaining cards out of 50 cards.

The probability that the second card is the same as the first card is equivalent of choosing 1 out 1 remaining card out of 49 cards.

So the answer is simply $\frac3{51} \times \frac2{50} \times \frac1{49}$ .

Pi Han Goh - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$