SOLUTION: Excluding the jokers, what is the probability of drawing three cards with different mark? The answer is 169/425. Please kindly teach me how to find the answer. Thank you in advance

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Question 935875: Excluding the jokers, what is the probability of drawing three cards with different mark? The answer is 169/425. Please kindly teach me how to find the answer. Thank you in advance!
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
We don't understand what you mean by "different marks".

If you meant three cards like these, different ranks and different suits:

J, 3♦, 8,

then there are 13C3 ways to choose the 3 ranks, and for each of those ways,
there are 4 suits to give the lowest-ranked card, and for each of those ways,
there are 3 suits remaining to give the card with the middle-rank, and
2 suits remaining to give to the highest-ranked card.

The numerator of the probability would be (13C3)(4)(3)(2) = 286*24 = 6864.

The denominator would be the number of ways to select any 3 cards, or 52C3,
or 22100.

That would be a probability of  which reduces to ,
not .

So we must be misinterpreting what you mean by "different marks".

Sorry.

Edwin

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