Question 935875
<pre>
We don't understand what you mean by "different marks".

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

J<font color="red"><b>&#9829;</b></font>, 3<font color="red"><b>&#9830;</b></font>&#9830;, 8<b>&#9827;</b>,

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 {{{6864/22100}}} which reduces to {{{132/425}}},
not {{{169/425}}}.

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

Sorry.

Edwin</pre>